Graduate Logic Seminar

The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.

When: Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).
Where: Van Vleck B235 (unless otherwise announced).
Organizers: Mariya Soskava

Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.

Spring 2018

January 29, Organizational meeting

This day we decided the schedule for the semester.

February 5, Uri Andrews

Title: Building Models of Strongly Minimal Theories - Part 1

Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.

February 12, James Hanson

Title: Finding Definable Sets in Continuous Logic

Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable, omega-categorical, and other small theories.

February 19, Noah Schweber

Title: Proper forcing

Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly. Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property) were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and sketch some applications.

February 26, Patrick Nicodemus

Title: A survey of computable and constructive mathematics in economic history

March 5, Tamvana Makulumi

Title: Convexly Orderable Groups

March 12, Dan Turetsky (University of Notre Dame)

Title: Structural Jump

March 19, Ethan McCarthy

Title: Networks and degrees of points in non-second countable spaces

April 2, Wil Cocke

Title: Characterizing Finite Nilpotent Groups via Word Maps

Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.

April 9, Tejas Bhojraj

Title: Quantum Randomness

Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based.

April 16, Iván Ongay-Valverde

Title: What can we say about sets made by the union of Turing equivalence classes?

Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?

This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.

This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).

April 23, Ethan McCarthy (Thesis Defense) Start 3:45 Room B231

Title: Cototal enumeration degrees and their applications to effective mathematics

Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees.

Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on [math]\displaystyle{ \omega^{\lt \omega} }[/math], and as the degrees of enumeration-pointed trees on [math]\displaystyle{ 2^{\lt \omega} }[/math], and we will remark on some additional applications of these characterizations.

April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde

Title: Definibility of the Frobenius orbits and an application to sets of rational distances.

Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).

Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.

Fall 2017

September 11, Organizational meeting

This day we decided the schedule for the semester.

September 18, Noah Schweber

Title: The Kunen inconsistency

Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a nontrivial elementary embedding from V into some inner model M.

There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.

I'll present this argument, and talk a bit about the role of choice.

September 25, Noah Schweber

Title: Hindman's theorem via ultrafilters

Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.

October 2, James Hanson

Title: The Gromov-Hausdorff metric on type space in continuous logic

Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.

October 9, James Hanson

Title: Morley rank and stability in continuous logic

Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define > the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.

October 23, Tamvana Makulumi

Title: Boxy sets in ordered convexly-orderable structures.

October 30, Iván Ongay-Valverde

Title: Dancing SCCA and other Coloring Axioms

Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.

November 6, Wil Cocke

Title: Two new characterizations of nilpotent groups

Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.

Or...

Title: Centralizing Propagating Properties of Groups

Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples.

November 13, Steffen Lempp

Title: The computational complexity of properties of finitely presented groups

Abstract: I will survey index set complexity results on finitely presented groups.

November 20, Ethan McCarthy

Title: Strong Difference Randomness

Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms.

December 4, Tejas Bhojraj

Title: Quantum Algorithmic Randomness

Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.

December 11, Grigory Terlov

Title: The Logic of Erdős–Rényi Graphs

Previous Years

The schedule of talks from past semesters can be found here.

( ! ) Deprecated: Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34] in /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php on line 381
Call Stack
#	Time	Memory	Function	Location
1	0.0003	357600	{main}( )	.../index.php:0
2	0.0495	1478384	wfIndexMain( )	.../index.php:46
3	0.0496	1478496	MediaWiki->run( )	.../index.php:50
4	0.0496	1478496	MediaWiki->main( )	.../MediaWiki.php:562
5	0.0597	1607448	MediaWiki->performRequest( )	.../MediaWiki.php:904
6	0.0693	1663408	MediaWiki->performAction( $article = class Article { protected $mContext = class RequestContext { private $request = class WebRequest { ... }; private $title = class Title { ... }; private $wikipage = class WikiPage { ... }; private $action = 'view'; private $output = class OutputPage { ... }; private $user = class User { ... }; private $authority = NULL; private $lang = class LanguageEn { ... }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { ... }; private $timing = NULL; private $config = class GlobalVarConfig { ... }; private $languageRecursion = FALSE }; protected $mPage = class WikiPage { protected $mTitle = class Title { ... }; protected $mDataLoaded = TRUE; private $mPageIsRedirectField = FALSE; private $mHasRedirectTarget = NULL; protected $mRedirectTarget = NULL; private $mIsNew = FALSE; private $mIsRedirect = FALSE; protected $mLatest = 25640; protected $mPreparedEdit = FALSE; protected $mId = 1395; protected $mDataLoadedFrom = 0; private $mLastRevision = class MediaWiki\Revision\RevisionStoreRecord { ... }; protected $mTimestamp = '20231127031859'; protected $mTouched = '20231127031859'; protected $mLanguage = NULL; protected $mLinksUpdated = '20231127031859'; private $derivedDataUpdater = NULL }; public $mOldId = 15476; public $mRedirectedFrom = NULL; public $mRedirectUrl = FALSE; private $fetchResult = class Status { protected $ok = TRUE; protected $errors = [...]; public $value = class MediaWiki\Revision\RevisionStoreRecord { ... }; public $success = [...]; public $successCount = 0; public $failCount = 0; public $cleanCallback = FALSE; protected $messageLocalizer = NULL }; public $mParserOutput = NULL; protected $viewIsRenderAction = FALSE; protected $linkRenderer = class MediaWiki\Linker\LinkRenderer { private $forceArticlePath = FALSE; private $expandUrls = FALSE; private $comment = FALSE; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $revisionStore = class MediaWiki\Revision\RevisionStore { private $blobStore = class MediaWiki\Storage\SqlBlobStore { ... }; private $wikiId = FALSE; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $cache = class WANObjectCache { ... }; private $localCache = class EmptyBagOStuff { ... }; private $commentStore = class CommentStore { ... }; private $actorMigration = class ActorMigration { ... }; private $actorStore = class MediaWiki\User\ActorStore { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $contentModelStore = class MediaWiki\Storage\NameTableStore { ... }; private $slotRoleStore = class MediaWiki\Storage\NameTableStore { ... }; private $slotRoleRegistry = class MediaWiki\Revision\SlotRoleRegistry { ... }; private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $pageStore = class MediaWiki\Page\PageStore { ... }; private $titleFactory = class TitleFactory { ... } }; private $watchlistManager = class MediaWiki\Watchlist\WatchlistManager { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $readOnlyMode = class ReadOnlyMode { ... }; private $revisionLookup = class MediaWiki\Revision\RevisionStore { ... }; private $talkPageNotificationManager = class MediaWiki\User\TalkPageNotificationManager { ... }; private $watchedItemStore = class WatchedItemStore { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $wikiPageFactory = class MediaWiki\Page\WikiPageFactory { ... }; private $notificationTimestampCache = [...] }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $mRevisionRecord = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 15476; protected $mPageId = 1395; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20180427145424'; protected $mDeleted = 0; protected $mSize = 13509; protected $mSha1 = 'icvvfq3plyjtbfm0tbw6wc1ivl67jyg'; protected $mParentId = 15474; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE } }, $requestTitle = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = 25640; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Graduate Logic Seminar'; protected $mLength = 10656; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE } )	.../MediaWiki.php:322
7	0.0696	1663616	ViewAction->show( )	.../MediaWiki.php:542
8	0.0702	1663704	Article->view( )	.../ViewAction.php:78
9	0.1031	2185800	Article->generateContentOutput( $performer = class User { public $mId = 0; public $mName = '44.197.101.251'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231128215548'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { protected $data = [...]; protected $queryAndPathParams = [...]; protected $queryParams = [...]; protected $headers = [...]; private $response = class WebResponse { ... }; private $ip = '44.197.101.251'; protected $requestTime = 1701208548.8541; protected $protocol = 'http'; protected $sessionId = class MediaWiki\Session\SessionId { ... }; protected $markedAsSafe = FALSE }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { private $permissionManager = class MediaWiki\Permissions\PermissionManager { ... }; private $actor = ...; private $userBlock = NULL }; private $isTemp = NULL }, $parserOptions = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '44.197.101.251'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231128215548'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $oldid = 15476, $outputPage = class OutputPage { private ${ContextSource}context = class RequestContext { private $request = class WebRequest { ... }; private $title = class Title { ... }; private $wikipage = class WikiPage { ... }; private $action = 'view'; private $output = ...; private $user = class User { ... }; private $authority = NULL; private $lang = class LanguageEn { ... }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { ... }; private $timing = NULL; private $config = class GlobalVarConfig { ... }; private $languageRecursion = FALSE }; protected $mMetatags = []; protected $mLinktags = []; protected $mCanonicalUrl = FALSE; private $mPageTitle = '<span class="mw-page-title-main">Graduate Logic Seminar</span>'; private $displayTitle = NULL; private $cacheIsFinal = FALSE; public $mBodytext = ''; private $mHTMLtitle = 'Graduate Logic Seminar - UW-Math Wiki'; private $mIsArticle = TRUE; private $mIsArticleRelated = TRUE; private $mHasCopyright = FALSE; private $mPrintable = FALSE; private $mSections = []; private $mSubtitle = [0 => '<div class="mw-message-box-warning mw-revision mw-message-box"><div id="mw-revision-info">Revision as of 14:54, 27 April 2018 by <a href="/index.php?title=User:Msoskova&action=edit&redlink=1" class="new mw-userlink" title="User:Msoskova (page does not exist)"><bdi>Msoskova</bdi></a> <span class="mw-usertoollinks">(<a href="/index.php?title=User_talk:Msoskova&action=edit&redlink=1" class="new mw-usertoollinks-talk" title="User talk:Msoskova (page does not exist)">talk</a> \| <a href="/index.ph'...]; public $mRedirect = ''; protected $mStatusCode = NULL; protected $mLastModified = 'Mon, 27 Nov 2023 03:18:59 GMT'; protected $mCategoryLinks = []; protected $mCategories = ['hidden' => [...], 'normal' => [...]]; protected $mIndicators = []; private $mLanguageLinks = []; private $mScripts = ''; protected $mInlineStyles = ''; public $mPageLinkTitle = ''; protected $mAdditionalHtmlClasses = []; protected $mHeadItems = []; protected $mAdditionalBodyClasses = []; protected $mModules = []; protected $mModuleStyles = [0 => 'mediawiki.action.styles', 1 => 'mediawiki.interface.helpers.styles']; protected $mResourceLoader = NULL; private $rlClient = NULL; private $rlClientContext = NULL; private $rlExemptStyleModules = NULL; protected $mJsConfigVars = ['wgSmjUseCdn' => FALSE, 'wgSmjUseChem' => TRUE, 'wgSmjDisplayMath' => [...], 'wgSmjExtraInlineMath' => [...], 'wgSmjScale' => 1.5, 'wgSmjEnableMenu' => TRUE, 'wgSmjDisplayAlign' => 'left']; protected $mTemplateIds = []; protected $mImageTimeKeys = []; public $mRedirectCode = ''; protected $mFeedLinksAppendQuery = NULL; protected $mAllowedModules = ['combined' => 10]; protected $mDoNothing = FALSE; protected $mParserOptions = NULL; private $mFeedLinks = []; protected $mEnableClientCache = TRUE; private $mArticleBodyOnly = FALSE; protected $mNewSectionLink = FALSE; protected $mHideNewSectionLink = FALSE; public $mNoGallery = FALSE; protected $mCdnMaxage = 0; protected $mCdnMaxageLimit = INF; protected $mPreventClickjacking = FALSE; private $mRevisionId = 15476; private $mRevisionIsCurrent = FALSE; private $mRevisionTimestamp = '20180427145424'; protected $mFileVersion = NULL; protected $styles = []; private $mIndexPolicy = 'index'; private $mFollowPolicy = 'follow'; private $mRobotsOptions = []; private $mVaryHeader = ['Accept-Encoding' => NULL]; private $mRedirectedFrom = NULL; private $mProperties = []; private $mTarget = NULL; private $mEnableTOC = FALSE; private $copyrightUrl = NULL; private $limitReportJSData = []; private $contentOverrides = []; private $contentOverrideCallbacks = []; private $mLinkHeader = []; private $CSP = class ContentSecurityPolicy { private $nonce = NULL; private $mwConfig = class GlobalVarConfig { ... }; private $response = class WebResponse { ... }; private $extraDefaultSrc = [...]; private $extraScriptSrc = [...]; private $extraStyleSrc = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } } }, $textOptions = ['skin' => class MediaWiki\Skins\Vector\SkinVectorLegacy { private ${ContextSource}context = class RequestContext { ... }; private ${Skin}defaultLinkOptions = [...]; protected $skinname = 'vector'; protected $options = [...]; protected $mRelevantTitle = NULL; private ${Skin}mRelevantUser = FALSE; private ${Skin}languageLinks = NULL; private ${Skin}sidebar = NULL; private ${Skin}componentRegistry = class MediaWiki\Skin\SkinComponentRegistry { ... }; public $template = NULL; public $thispage = NULL; public $titletxt = NULL; public $userpage = NULL; public $thisquery = NULL; public $loggedin = NULL; public $username = NULL; public $userpageUrlDetails = NULL; private ${SkinTemplate}isTempUser = NULL; private ${SkinTemplate}isNamedUser = NULL; private ${SkinTemplate}templateContextSet = FALSE; private ${SkinTemplate}contentNavigationCached = NULL; private ${SkinMustache}templateParser = NULL; private ${MediaWiki\Skins\Vector\SkinVector}languages = NULL }, 'injectTOC' => TRUE, 'enableSectionEditLinks' => FALSE, 'includeDebugInfo' => TRUE] )	.../Article.php:528
10	0.1300	2434192	MediaWiki\Page\ParserOutputAccess->getParserOutput( $page = class WikiPage { protected $mTitle = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = 25640; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Graduate Logic Seminar'; protected $mLength = 10656; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; protected $mDataLoaded = TRUE; private $mPageIsRedirectField = FALSE; private $mHasRedirectTarget = NULL; protected $mRedirectTarget = NULL; private $mIsNew = FALSE; private $mIsRedirect = FALSE; protected $mLatest = 25640; protected $mPreparedEdit = FALSE; protected $mId = 1395; protected $mDataLoadedFrom = 0; private $mLastRevision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 25640; protected $mPageId = 1395; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20231127031859'; protected $mDeleted = 0; protected $mSize = 10656; protected $mSha1 = 'gv6ftllkokclkdlnljrg87yd28zg42h'; protected $mParentId = 25620; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = TRUE }; protected $mTimestamp = '20231127031859'; protected $mTouched = '20231127031859'; protected $mLanguage = NULL; protected $mLinksUpdated = '20231127031859'; private $derivedDataUpdater = NULL }, $parserOptions = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '44.197.101.251'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231128215548'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 15476; protected $mPageId = 1395; protected $mUser = class MediaWiki\User\UserIdentityValue { private $id = 829; private $name = 'Msoskova'; private $wikiId = FALSE }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20180427145424'; protected $mDeleted = 0; protected $mSize = 13509; protected $mSha1 = 'icvvfq3plyjtbfm0tbw6wc1ivl67jyg'; protected $mParentId = 15474; protected $mComment = class CommentStoreComment { public $id = '1'; public $text = ''; public $message = class RawMessage { ... }; public $data = NULL }; protected $mPage = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { protected $slots = [...] }; protected $mCurrent = FALSE }, $options = 5 )	.../Article.php:713
11	0.1304	2434976	PoolCounterWork->execute( $skipcache = ??? )	.../ParserOutputAccess.php:299
12	0.1304	2435168	PoolWorkArticleViewOld->doWork( )	.../PoolCounterWork.php:162
13	0.1305	2435424	PoolWorkArticleView->renderRevision( )	.../PoolWorkArticleViewOld.php:66
14	0.1306	2438448	MediaWiki\Revision\RenderedRevision->getRevisionParserOutput( $hints = ??? )	.../PoolWorkArticleView.php:91
15	0.1306	2438448	call_user_func:{/var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php:199}( $callback = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $roleRegistery = class MediaWiki\Revision\SlotRoleRegistry { ... }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { ... }; private $dbDomain = FALSE }; public $parameter = ['$rrev' => '<required>', '$hints' => '<required>'] }, $args = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 15476; protected $mPageId = 1395; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20180427145424'; protected $mDeleted = 0; protected $mSize = 13509; protected $mSha1 = 'icvvfq3plyjtbfm0tbw6wc1ivl67jyg'; protected $mParentId = 15474; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, [] )	.../RenderedRevision.php:199
16	0.1306	2438520	MediaWiki\Revision\RevisionRenderer->MediaWiki\Revision\{closure:/var/www/wiki_mediawiki-1.39.3/includes/Revision/RevisionRenderer.php:157-159}( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 15476; protected $mPageId = 1395; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20180427145424'; protected $mDeleted = 0; protected $mSize = 13509; protected $mSha1 = 'icvvfq3plyjtbfm0tbw6wc1ivl67jyg'; protected $mParentId = 15474; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, $hints = [] )	.../RenderedRevision.php:199
17	0.1306	2438520	MediaWiki\Revision\RevisionRenderer->combineSlotOutput( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 15476; protected $mPageId = 1395; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20180427145424'; protected $mDeleted = 0; protected $mSize = 13509; protected $mSha1 = 'icvvfq3plyjtbfm0tbw6wc1ivl67jyg'; protected $mParentId = 15474; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, $hints = [] )	.../RevisionRenderer.php:158
18	0.1316	2440096	MediaWiki\Revision\RenderedRevision->getSlotParserOutput( $role = 'main', $hints = [] )	.../RevisionRenderer.php:221
19	0.1403	2457984	MediaWiki\Revision\RenderedRevision->getSlotParserOutputUncached( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...; private $redirectTargetAndText = [0 => NULL, 1 => 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...]; private $preSaveTransformFlags = [] }, $withHtml = TRUE )	.../RenderedRevision.php:237
20	0.1403	2457984	MediaWiki\Content\Renderer\ContentRenderer->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...; private $redirectTargetAndText = [0 => NULL, 1 => 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...]; private $preSaveTransformFlags = [] }, $page = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $revId = 15476, $parserOptions = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '44.197.101.251'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231128215548'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $generateHtml = TRUE )	.../RenderedRevision.php:265
21	0.1404	2458096	ContentHandler->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...; private $redirectTargetAndText = [0 => NULL, 1 => 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $revId = 15476; private $parserOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $generateHtml = TRUE } )	.../ContentRenderer.php:47
22	0.1406	2460192	WikitextContentHandler->fillParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...; private $redirectTargetAndText = [0 => NULL, 1 => 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $revId = 15476; private $parserOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $generateHtml = TRUE }, $parserOutput = class ParserOutput { protected $mParseUsedOptions = []; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = []; private $mCategories = []; private $mIndicators = []; private $mTitleText = ''; private $mLinks = []; private $mLinksSpecial = []; private $mTemplates = []; private $mTemplateIds = []; private $mImages = []; private $mFileSearchOptions = []; private $mExternalLinks = []; private $mInterwikiLinks = []; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = []; private $mModules = []; private $mModuleStyles = []; private $mJsConfigVars = []; private $mOutputHooks = []; private $mWarnings = []; private $mWarningMsgs = []; private $mSections = []; private $mProperties = []; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = []; private $mLimitReportData = []; private $mLimitReportJSData = []; private $mCacheMessage = ''; private $mParseStartTime = []; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = []; private $mExtraDefaultSrcs = []; private $mExtraStyleSrcs = []; private $mFlags = []; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = []; private $mMaxAdaptiveExpiry = INF } )	.../ContentHandler.php:1720
23	0.1406	2460192	Parser->parse( $text = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'..., $page = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $options = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '44.197.101.251'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231128215548'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $linestart = TRUE, $clearState = TRUE, $revid = 15476 )	.../WikitextContentHandler.php:301
24	0.1407	2467464	Parser->internalParse( $text = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'..., $isMain = ???, $frame = ??? )	.../Parser.php:724
25	0.1407	2467496	Parser->replaceVariables( $text = 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'..., $frame = ???, $argsOnly = ??? )	.../Parser.php:1610
26	0.1432	2531296	PPFrame_Hash->expand( $root = class PPNode_Hash_Tree { public $name = 'root'; private $rawChildren = [0 => 'The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning materials that are not usually presented on a class.\n\n* \'\'\'When:\'\'\' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).\n* \'\'\'Where:\'\'\' Van Vleck B235 (unless otherwise announced).\n* \'\'\'Organizers:\'\'\' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava'..., 1 => [...], 2 => '\n\n', 3 => [...], 4 => '\n\nThis day we decided the schedule for the semester.\n\n', 5 => [...], 6 => '\n\nTitle: Building Models of Strongly Minimal Theories - Part 1\n\nAbstract: Since I\'m talking in the Tuesday seminar as well, I\'ll use the Monday seminar talk to do some background on the topic and some\nlemmas that will go into the proofs in Tuesday\'s talk. There will be (I hope) some theorems of interest to see on both days, and both on\nthe general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute\ncopies of all of its countable models. I\'l'..., 7 => [...], 8 => '\n\nTitle: Finding Definable Sets in Continuous Logic\n\nAbstract: In order to be useful the notion of a \'definable set\' in continuous logic is stricter than a naive comparison to discrete logic\nwould suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a\nsuperstable theory with no non-trivial definable sets. As we\'ll see, however, there are many definable sets in omega-stable,\nomega-categorical, and other small theories.\n\n', 9 => [...], 10 => '\n\nTitle: Proper forcing\n\nAbstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.\nEarly preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)\nwere fairly limited, and things really got off the ground with Shelah\'s invention of "proper forcing." Roughly speaking, a forcing is\nproper if it can be approximated by elementary submodels of the universe in a part'..., 11 => [...], 12 => '\n\nTitle: A survey of computable and constructive mathematics in economic history\n\n', 13 => [...], 14 => '\n\nTitle: Convexly Orderable Groups \n\n', 15 => [...], 16 => '\n\nTitle: Structural Jump\n\n', 17 => [...], 18 => '\n\nTitle: Networks and degrees of points in non-second countable spaces\n\n', 19 => [...], 20 => '\n\nTitle: Characterizing Finite Nilpotent Groups via Word Maps\n\nAbstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.\n\n', 21 => [...], 22 => '\n\nTitle: Quantum Randomness\n\nAbstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based. \n\n', 23 => [...], 24 => '\n\nTitle: What can we say about sets made by the union of Turing equivalence classes?\n\nAbstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type \'the rationals\' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes'..., 25 => [...], 26 => '\n\nTitle: Cototal enumeration degrees and their applications to effective mathematics \n\nAbstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natur'..., 27 => [...], 28 => ', and as the degrees of enumeration-pointed trees on ', 29 => [...], 30 => ', and we will remark on some additional applications of these characterizations.\n\n', 31 => [...], 32 => '\n\nTitle: Definibility of the Frobenius orbits and an application to sets of rational distances.\n\nAbstract: In this talk I\'ll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert\'s tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).\n\nFinally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational d'..., 33 => [...], 34 => '\n\n', 35 => [...], 36 => '\n\nThis day we decided the schedule for the semester.\n\n', 37 => [...], 38 => '\n\nTitle: The Kunen inconsistency\n\nAbstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey\'s\ntheorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the\nwhole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a\nnontrivial elementary embedding from V into some inner model M.\n\nThere are several var'..., 39 => [...], 40 => '\n\nTitle: Hindman\'s theorem via ultrafilters\n\nAbstract: Hindman\'s theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any finite sum from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman\'s theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We\'ll do.\n\n', 41 => [...], 42 => '\n\nTitle: The Gromov-Hausdorff metric on type space in continuous logic\n\nAbstract: The Gromov-Hausdorff metric is a notion of the \'distance\' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is sligh'..., 43 => [...], 44 => '\n\nTitle: Morley rank and stability in continuous logic\n\nAbstract: There are various ways of counting the \'size\' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define\n> the \'correct\' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we\'ll prove that inseparably categorical theor'..., 45 => [...], 46 => '\n\nTitle: Boxy sets in ordered convexly-orderable structures.\n\n', 47 => [...], 48 => '\n\nTitle: Dancing SCCA and other Coloring Axioms\n\nAbstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I\'m happy to discuss.\n\n', 49 => [...], 50 => '\n\nTitle: Two new characterizations of nilpotent groups\n\nAbstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.\n\nOr...\n\nTitle: Centralizing Propagating Properties of Groups\n\nAbstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples. \n\n', 51 => [...], 52 => '\n\nTitle: The computational complexity of properties of finitely presented groups\n\nAbstract: I will survey index set complexity results on finitely presented groups.\n\n', 53 => [...], 54 => '\n\nTitle: Strong Difference Randomness\n\nAbstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms. \n\n', 55 => [...], 56 => '\n\nTitle: Quantum Algorithmic Randomness\n\nAbstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.\n\n', 57 => [...], 58 => '\n\nTitle: The Logic of Erdős–Rényi Graphs\n\n', 59 => [...], 60 => '\n\nThe schedule of talks from past semesters can be found ', 61 => '[[Logic Graduate Seminar, previous semesters\|here]].']; private $store = [0 => [...]]; private $index = 0 }, $flags = 0 )	.../Parser.php:2955
27	0.1436	2546040	Parser->extensionSubstitution( $params = ['name' => class PPNode_Hash_Tree { public $name = 'name'; private $rawChildren = [...]; private $store = [...]; private $index = 0 }, 'attr' => class PPNode_Hash_Tree { public $name = 'attr'; private $rawChildren = [...]; private $store = [...]; private $index = 1 }, 'inner' => class PPNode_Hash_Tree { public $name = 'inner'; private $rawChildren = [...]; private $store = [...]; private $index = 2 }, 'close' => class PPNode_Hash_Tree { public $name = 'close'; private $rawChildren = [...]; private $store = [...]; private $index = 3 }], $frame = class PPFrame_Hash { public $parser = class Parser { private $mTagHooks = [...]; private $mFunctionHooks = [...]; private $mFunctionSynonyms = [...]; private $mStripList = [...]; private $mVarCache = [...]; private $mImageParams = [...]; private $mImageParamsMagicArray = [...]; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { ... }; private $mSubstWords = class MagicWordArray { ... }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]*?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $mPreprocessor = class Preprocessor_Hash { ... }; private $mOutput = class ParserOutput { ... }; private $mAutonumber = 0; private $mStripState = class StripState { ... }; private $mLinkHolders = class LinkHolderArray { ... }; private $mLinkID = 0; private $mIncludeSizes = [...]; public $mPPNodeCount = 17; public $mHighestExpansionDepth = 2; private $mTplRedirCache = [...]; public $mHeadings = [...]; private $mDoubleUnderscores = [...]; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = [...]; private $mUser = NULL; public $mOptions = class ParserOptions { ... }; public $mTitle = class Title { ... }; private $mOutputType = 1; public $ot = [...]; private $mRevisionId = 15476; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13509; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = [...]; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { ... }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $factory = class ParserFactory { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $preprocessor = class Preprocessor_Hash { public $parser = class Parser { ... }; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; public $title = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $titleCache = [0 => 'Graduate_Logic_Seminar']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 }, $processNowiki = FALSE )	.../PPFrame_Hash.php:353
28	0.1436	2546544	SimpleMathJaxHooks::renderMath( $tex = '\\omega^{<\\omega}', $args = [], $parser = class Parser { private $mTagHooks = ['pre' => [...], 'nowiki' => [...], 'gallery' => [...], 'indicator' => [...], 'langconvert' => [...], 'math' => 'SimpleMathJaxHooks::renderMath', 'chem' => 'SimpleMathJaxHooks::renderChem', 'source' => [...], 'syntaxhighlight' => [...], 'ref' => [...], 'references' => [...]]; private $mFunctionHooks = ['ns' => [...], 'nse' => [...], 'urlencode' => [...], 'lcfirst' => [...], 'ucfirst' => [...], 'lc' => [...], 'uc' => [...], 'localurl' => [...], 'localurle' => [...], 'fullurl' => [...], 'fullurle' => [...], 'canonicalurl' => [...], 'canonicalurle' => [...], 'formatnum' => [...], 'grammar' => [...], 'gender' => [...], 'plural' => [...], 'bidi' => [...], 'numberofpages' => [...], 'numberofusers' => [...], 'numberofactiveusers' => [...], 'numberofarticles' => [...], 'numberoffiles' => [...], 'numberofadmins' => [...], 'numberingroup' => [...], 'numberofedits' => [...], 'language' => [...], 'padleft' => [...], 'padright' => [...], 'anchorencode' => [...], 'defaultsort' => [...], 'filepath' => [...], 'pagesincategory' => [...], 'pagesize' => [...], 'protectionlevel' => [...], 'protectionexpiry' => [...], 'namespace' => [...], 'namespacee' => [...], 'namespacenumber' => [...], 'talkspace' => [...], 'talkspacee' => [...], 'subjectspace' => [...], 'subjectspacee' => [...], 'pagename' => [...], 'pagenamee' => [...], 'fullpagename' => [...], 'fullpagenamee' => [...], 'rootpagename' => [...], 'rootpagenamee' => [...], 'basepagename' => [...], 'basepagenamee' => [...], 'subpagename' => [...], 'subpagenamee' => [...], 'talkpagename' => [...], 'talkpagenamee' => [...], 'subjectpagename' => [...], 'subjectpagenamee' => [...], 'pageid' => [...], 'revisionid' => [...], 'revisionday' => [...], 'revisionday2' => [...], 'revisionmonth' => [...], 'revisionmonth1' => [...], 'revisionyear' => [...], 'revisiontimestamp' => [...], 'revisionuser' => [...], 'cascadingsources' => [...], 'int' => [...], 'special' => [...], 'speciale' => [...], 'tag' => [...], 'formatdate' => [...], 'displaytitle' => [...]]; private $mFunctionSynonyms = [0 => [...], 1 => [...]]; private $mStripList = [0 => 'pre', 1 => 'nowiki', 2 => 'gallery', 3 => 'indicator', 4 => 'langconvert', 5 => 'math', 6 => 'chem', 7 => 'source', 8 => 'syntaxhighlight', 9 => 'ref', 10 => 'references']; private $mVarCache = []; private $mImageParams = []; private $mImageParamsMagicArray = []; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = [...]; private $baseRegex = NULL; private $regex = NULL }; private $mSubstWords = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = NULL; private $baseRegex = [...]; private $regex = NULL }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { private $server = 'https://wiki.math.wisc.edu'; private $canonicalServer = 'https://wiki.math.wisc.edu'; private $internalServer = 'https://wiki.math.wisc.edu'; private $fallbackProtocol = 'http'; private $httpsPort = 443; private $validProtocols = [...]; private $validProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/'; private $validAbsoluteProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:' }; private $mPreprocessor = class Preprocessor_Hash { public $parser = ...; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; private $mOutput = class ParserOutput { protected $mParseUsedOptions = [...]; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = [...]; private $mCategories = [...]; private $mIndicators = [...]; private $mTitleText = ''; private $mLinks = [...]; private $mLinksSpecial = [...]; private $mTemplates = [...]; private $mTemplateIds = [...]; private $mImages = [...]; private $mFileSearchOptions = [...]; private $mExternalLinks = [...]; private $mInterwikiLinks = [...]; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = [...]; private $mModules = [...]; private $mModuleStyles = [...]; private $mJsConfigVars = [...]; private $mOutputHooks = [...]; private $mWarnings = [...]; private $mWarningMsgs = [...]; private $mSections = [...]; private $mProperties = [...]; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = [...]; private $mLimitReportData = [...]; private $mLimitReportJSData = [...]; private $mCacheMessage = ''; private $mParseStartTime = [...]; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = [...]; private $mExtraDefaultSrcs = [...]; private $mExtraStyleSrcs = [...]; private $mFlags = [...]; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = [...]; private $mMaxAdaptiveExpiry = INF }; private $mAutonumber = 0; private $mStripState = class StripState { protected $data = [...]; protected $regex = '/\'"`UNIQ-([^<>&\'"]+)-QINU`"\'/'; protected $parser = ...; protected $circularRefGuard = [...]; protected $depth = 0; protected $highestDepth = 0; protected $expandSize = 0; protected $depthLimit = 20; protected $sizeLimit = 5000000 }; private $mLinkHolders = class LinkHolderArray { public $internals = [...]; public $interwikis = [...]; public $size = 0; public $parent = ...; private $languageConverter = class TrivialLanguageConverter { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $mLinkID = 0; private $mIncludeSizes = ['post-expand' => 0, 'arg' => 0]; public $mPPNodeCount = 17; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...], 2 => [...], 3 => [...], 4 => [...], 5 => [...], 6 => [...], 7 => [...], 8 => [...], 9 => [...], 10 => [...], 11 => [...], 12 => [...]]; private $mDoubleUnderscores = []; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = []; private $mUser = NULL; public $mOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; public $mTitle = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $mOutputType = 1; public $ot = ['html' => TRUE, 'wiki' => FALSE, 'pre' => FALSE, 'plain' => FALSE]; private $mRevisionId = 15476; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13509; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = []; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { protected $start = NULL; protected $end = NULL; protected $stack = [...]; protected $workStack = [...]; protected $collated = [...]; protected $collateDone = FALSE; protected $errorEntry = [...]; protected $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { private $mVariableIDsInitialised = TRUE; private $mVariableIDs = [...]; private $mCacheTTLs = [...]; private $mDoubleUnderscoreIDs = [...]; private $mSubstIDs = [...]; private $mObjects = [...]; private $mDoubleUnderscoreArray = class MagicWordArray { ... }; private $contLang = class LanguageEn { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $contLang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = NULL; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = [...]; private ${Language}namespaceInfo = class NamespaceInfo { ... }; private ${Language}localisationCache = class LocalisationCache { ... }; private ${Language}langNameUtils = class MediaWiki\Languages\LanguageNameUtils { ... }; private ${Language}langFallback = class MediaWiki\Languages\LanguageFallback { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private ${Language}hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private ${Language}hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private ${Language}config = class GlobalVarConfig { ... } }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { private $cache = [...]; private $converterList = [...]; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $isConversionDisabled = FALSE; private $isTitleConversionDisabled = FALSE; private $defaultLanguage = class Closure { ... } }; private $factory = class ParserFactory { private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $wanCache = class WANObjectCache { ... }; private $mainInstance = ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { private $list = [...]; private $aliases = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contLang = class LanguageEn { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $titleFactory = class TitleFactory { ... } }; private $titleFormatter = class MediaWikiTitleCodec { protected $language = class LanguageEn { ... }; protected $genderCache = class GenderCache { ... }; protected $localInterwikis = [...]; protected $interwikiLookup = class MediaWiki\Interwiki\ClassicInterwikiLookup { ... }; protected $nsInfo = class NamespaceInfo { ... }; private $createMalformedTitleException = class Closure { ... } }; private $svcOptions = class MediaWiki\Config\ServiceOptions { private $keys = [...]; private $options = [...] }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $nsInfo = class NamespaceInfo { private $alwaysCapitalizedNamespaces = [...]; private $canonicalNamespaces = [...]; private $namespaceIndexes = [...]; private $validNamespaces = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $logger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'Parser'; private $minimumLevel = 999; private $isDB = FALSE }; private $badFileLookup = class MediaWiki\BadFileLookup { private $listCallback = class Closure { ... }; private $cache = class EmptyBagOStuff { ... }; private $repoGroup = class RepoGroup { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $badFiles = NULL; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { private $dynamicHandlers = [...]; private $tombstones = [...]; private $handlersByName = [...]; private $registry = class MediaWiki\HookContainer\GlobalHookRegistry { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $nextScopedRegisterId = 0 }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { private $container = class MediaWiki\HookContainer\HookContainer { ... } }; private $tidy = class MediaWiki\Tidy\RemexDriver { protected $config = [...]; private $treeMutationTrace = FALSE; private $serializerTrace = FALSE; private $mungerTrace = FALSE; private $pwrap = TRUE; private $enableLegacyMediaDOM = TRUE }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $userFactory = class MediaWiki\User\UserFactory { private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $lastUserFromIdentity = NULL }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $trackingCategories = class TrackingCategories { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $namespaceInfo = class NamespaceInfo { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $extensionRegistry = class ExtensionRegistry { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $parserFactoryClosure = class Closure { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFactory = class TitleFactory { ... } }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; protected $deprecatedPublicProperties = ['mLinkID' => [...], 'mIncludeSizes' => [...], 'mDoubleUnderscores' => [...], 'mShowToc' => [...], 'mRevisionId' => [...], 'mRevisionTimestamp' => [...], 'mRevisionUser' => [...], 'mRevisionSize' => [...], 'mInputSize' => [...], 'mInParse' => [...], 'mFirstCall' => [...], 'mGeneratedPPNodeCount' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $frame = class PPFrame_Hash { public $parser = class Parser { private $mTagHooks = [...]; private $mFunctionHooks = [...]; private $mFunctionSynonyms = [...]; private $mStripList = [...]; private $mVarCache = [...]; private $mImageParams = [...]; private $mImageParamsMagicArray = [...]; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { ... }; private $mSubstWords = class MagicWordArray { ... }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $mPreprocessor = class Preprocessor_Hash { ... }; private $mOutput = class ParserOutput { ... }; private $mAutonumber = 0; private $mStripState = class StripState { ... }; private $mLinkHolders = class LinkHolderArray { ... }; private $mLinkID = 0; private $mIncludeSizes = [...]; public $mPPNodeCount = 17; public $mHighestExpansionDepth = 2; private $mTplRedirCache = [...]; public $mHeadings = [...]; private $mDoubleUnderscores = [...]; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = [...]; private $mUser = NULL; public $mOptions = class ParserOptions { ... }; public $mTitle = class Title { ... }; private $mOutputType = 1; public $ot = [...]; private $mRevisionId = 15476; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13509; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = [...]; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { ... }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $factory = class ParserFactory { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $preprocessor = class Preprocessor_Hash { public $parser = class Parser { ... }; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; public $title = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $titleCache = [0 => 'Graduate_Logic_Seminar']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 } )	.../Parser.php:4023
29	0.1436	2546640	SimpleMathJaxHooks::renderTex( $tex = '\\displaystyle{ \\omega^{\\lt \\omega} }', $parser = class Parser { private $mTagHooks = ['pre' => [...], 'nowiki' => [...], 'gallery' => [...], 'indicator' => [...], 'langconvert' => [...], 'math' => 'SimpleMathJaxHooks::renderMath', 'chem' => 'SimpleMathJaxHooks::renderChem', 'source' => [...], 'syntaxhighlight' => [...], 'ref' => [...], 'references' => [...]]; private $mFunctionHooks = ['ns' => [...], 'nse' => [...], 'urlencode' => [...], 'lcfirst' => [...], 'ucfirst' => [...], 'lc' => [...], 'uc' => [...], 'localurl' => [...], 'localurle' => [...], 'fullurl' => [...], 'fullurle' => [...], 'canonicalurl' => [...], 'canonicalurle' => [...], 'formatnum' => [...], 'grammar' => [...], 'gender' => [...], 'plural' => [...], 'bidi' => [...], 'numberofpages' => [...], 'numberofusers' => [...], 'numberofactiveusers' => [...], 'numberofarticles' => [...], 'numberoffiles' => [...], 'numberofadmins' => [...], 'numberingroup' => [...], 'numberofedits' => [...], 'language' => [...], 'padleft' => [...], 'padright' => [...], 'anchorencode' => [...], 'defaultsort' => [...], 'filepath' => [...], 'pagesincategory' => [...], 'pagesize' => [...], 'protectionlevel' => [...], 'protectionexpiry' => [...], 'namespace' => [...], 'namespacee' => [...], 'namespacenumber' => [...], 'talkspace' => [...], 'talkspacee' => [...], 'subjectspace' => [...], 'subjectspacee' => [...], 'pagename' => [...], 'pagenamee' => [...], 'fullpagename' => [...], 'fullpagenamee' => [...], 'rootpagename' => [...], 'rootpagenamee' => [...], 'basepagename' => [...], 'basepagenamee' => [...], 'subpagename' => [...], 'subpagenamee' => [...], 'talkpagename' => [...], 'talkpagenamee' => [...], 'subjectpagename' => [...], 'subjectpagenamee' => [...], 'pageid' => [...], 'revisionid' => [...], 'revisionday' => [...], 'revisionday2' => [...], 'revisionmonth' => [...], 'revisionmonth1' => [...], 'revisionyear' => [...], 'revisiontimestamp' => [...], 'revisionuser' => [...], 'cascadingsources' => [...], 'int' => [...], 'special' => [...], 'speciale' => [...], 'tag' => [...], 'formatdate' => [...], 'displaytitle' => [...]]; private $mFunctionSynonyms = [0 => [...], 1 => [...]]; private $mStripList = [0 => 'pre', 1 => 'nowiki', 2 => 'gallery', 3 => 'indicator', 4 => 'langconvert', 5 => 'math', 6 => 'chem', 7 => 'source', 8 => 'syntaxhighlight', 9 => 'ref', 10 => 'references']; private $mVarCache = []; private $mImageParams = []; private $mImageParamsMagicArray = []; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = [...]; private $baseRegex = NULL; private $regex = NULL }; private $mSubstWords = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = NULL; private $baseRegex = [...]; private $regex = NULL }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]*?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { private $server = 'https://wiki.math.wisc.edu'; private $canonicalServer = 'https://wiki.math.wisc.edu'; private $internalServer = 'https://wiki.math.wisc.edu'; private $fallbackProtocol = 'http'; private $httpsPort = 443; private $validProtocols = [...]; private $validProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/'; private $validAbsoluteProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:' }; private $mPreprocessor = class Preprocessor_Hash { public $parser = ...; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; private $mOutput = class ParserOutput { protected $mParseUsedOptions = [...]; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = [...]; private $mCategories = [...]; private $mIndicators = [...]; private $mTitleText = ''; private $mLinks = [...]; private $mLinksSpecial = [...]; private $mTemplates = [...]; private $mTemplateIds = [...]; private $mImages = [...]; private $mFileSearchOptions = [...]; private $mExternalLinks = [...]; private $mInterwikiLinks = [...]; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = [...]; private $mModules = [...]; private $mModuleStyles = [...]; private $mJsConfigVars = [...]; private $mOutputHooks = [...]; private $mWarnings = [...]; private $mWarningMsgs = [...]; private $mSections = [...]; private $mProperties = [...]; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = [...]; private $mLimitReportData = [...]; private $mLimitReportJSData = [...]; private $mCacheMessage = ''; private $mParseStartTime = [...]; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = [...]; private $mExtraDefaultSrcs = [...]; private $mExtraStyleSrcs = [...]; private $mFlags = [...]; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = [...]; private $mMaxAdaptiveExpiry = INF }; private $mAutonumber = 0; private $mStripState = class StripState { protected $data = [...]; protected $regex = '/\'"`UNIQ-([^<>&\'"]+)-QINU`"\'/'; protected $parser = ...; protected $circularRefGuard = [...]; protected $depth = 0; protected $highestDepth = 0; protected $expandSize = 0; protected $depthLimit = 20; protected $sizeLimit = 5000000 }; private $mLinkHolders = class LinkHolderArray { public $internals = [...]; public $interwikis = [...]; public $size = 0; public $parent = ...; private $languageConverter = class TrivialLanguageConverter { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $mLinkID = 0; private $mIncludeSizes = ['post-expand' => 0, 'arg' => 0]; public $mPPNodeCount = 17; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...], 2 => [...], 3 => [...], 4 => [...], 5 => [...], 6 => [...], 7 => [...], 8 => [...], 9 => [...], 10 => [...], 11 => [...], 12 => [...]]; private $mDoubleUnderscores = []; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = []; private $mUser = NULL; public $mOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; public $mTitle = class Title { private $mTextform = 'Graduate Logic Seminar'; private $mUrlform = 'Graduate_Logic_Seminar'; private $mDbkeyform = 'Graduate_Logic_Seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1395; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $mOutputType = 1; public $ot = ['html' => TRUE, 'wiki' => FALSE, 'pre' => FALSE, 'plain' => FALSE]; private $mRevisionId = 15476; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13509; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = []; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { protected $start = NULL; protected $end = NULL; protected $stack = [...]; protected $workStack = [...]; protected $collated = [...]; protected $collateDone = FALSE; protected $errorEntry = [...]; protected $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { private $mVariableIDsInitialised = TRUE; private $mVariableIDs = [...]; private $mCacheTTLs = [...]; private $mDoubleUnderscoreIDs = [...]; private $mSubstIDs = [...]; private $mObjects = [...]; private $mDoubleUnderscoreArray = class MagicWordArray { ... }; private $contLang = class LanguageEn { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $contLang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = NULL; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = [...]; private ${Language}namespaceInfo = class NamespaceInfo { ... }; private ${Language}localisationCache = class LocalisationCache { ... }; private ${Language}langNameUtils = class MediaWiki\Languages\LanguageNameUtils { ... }; private ${Language}langFallback = class MediaWiki\Languages\LanguageFallback { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private ${Language}hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private ${Language}hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private ${Language}config = class GlobalVarConfig { ... } }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { private $cache = [...]; private $converterList = [...]; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $isConversionDisabled = FALSE; private $isTitleConversionDisabled = FALSE; private $defaultLanguage = class Closure { ... } }; private $factory = class ParserFactory { private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $wanCache = class WANObjectCache { ... }; private $mainInstance = ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { private $list = [...]; private $aliases = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contLang = class LanguageEn { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $titleFactory = class TitleFactory { ... } }; private $titleFormatter = class MediaWikiTitleCodec { protected $language = class LanguageEn { ... }; protected $genderCache = class GenderCache { ... }; protected $localInterwikis = [...]; protected $interwikiLookup = class MediaWiki\Interwiki\ClassicInterwikiLookup { ... }; protected $nsInfo = class NamespaceInfo { ... }; private $createMalformedTitleException = class Closure { ... } }; private $svcOptions = class MediaWiki\Config\ServiceOptions { private $keys = [...]; private $options = [...] }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $nsInfo = class NamespaceInfo { private $alwaysCapitalizedNamespaces = [...]; private $canonicalNamespaces = [...]; private $namespaceIndexes = [...]; private $validNamespaces = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $logger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'Parser'; private $minimumLevel = 999; private $isDB = FALSE }; private $badFileLookup = class MediaWiki\BadFileLookup { private $listCallback = class Closure { ... }; private $cache = class EmptyBagOStuff { ... }; private $repoGroup = class RepoGroup { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $badFiles = NULL; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { private $dynamicHandlers = [...]; private $tombstones = [...]; private $handlersByName = [...]; private $registry = class MediaWiki\HookContainer\GlobalHookRegistry { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $nextScopedRegisterId = 0 }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { private $container = class MediaWiki\HookContainer\HookContainer { ... } }; private $tidy = class MediaWiki\Tidy\RemexDriver { protected $config = [...]; private $treeMutationTrace = FALSE; private $serializerTrace = FALSE; private $mungerTrace = FALSE; private $pwrap = TRUE; private $enableLegacyMediaDOM = TRUE }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $userFactory = class MediaWiki\User\UserFactory { private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $lastUserFromIdentity = NULL }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $trackingCategories = class TrackingCategories { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $namespaceInfo = class NamespaceInfo { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $extensionRegistry = class ExtensionRegistry { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $parserFactoryClosure = class Closure { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFactory = class TitleFactory { ... } }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; protected $deprecatedPublicProperties = ['mLinkID' => [...], 'mIncludeSizes' => [...], 'mDoubleUnderscores' => [...], 'mShowToc' => [...], 'mRevisionId' => [...], 'mRevisionTimestamp' => [...], 'mRevisionUser' => [...], 'mRevisionSize' => [...], 'mInputSize' => [...], 'mInParse' => [...], 'mFirstCall' => [...], 'mGeneratedPPNodeCount' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE } )	.../SimpleMathJaxHooks.php:26
30	0.1437	2546640	ParserOutput->addModules( $modules = 'ext.SimpleMathJax' )	.../SimpleMathJaxHooks.php:34
31	0.1437	2546640	wfDeprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = ???, $callerOffset = ??? )	.../ParserOutput.php:1180
32	0.1437	2546640	MWDebug::deprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = FALSE, $callerOffset = 3 )	.../GlobalFunctions.php:765
33	0.1437	2546768	MWDebug::deprecatedMsg( $msg = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38.', $version = '1.38', $component = 'MediaWiki', $callerOffset = 4 )	.../MWDebug.php:233
34	0.1437	2548464	MWDebug::sendRawDeprecated( $msg = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34]', $sendToLog = TRUE, $callerFunc = 'SimpleMathJaxHooks::renderTex' )	.../MWDebug.php:351
35	0.1437	2548464	trigger_error( $message = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34]', $error_level = 16384 )	.../MWDebug.php:381

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0003	357600	{main}( )	.../index.php:0
2	0.0495	1478384	wfIndexMain( )	.../index.php:46
3	0.0496	1478496	MediaWiki->run( )	.../index.php:50
4	0.0496	1478496	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2534	2921792	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2535	2938368	WebResponse->header( $string = 'Content-type: text/html; charset=UTF-8', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2825
7	0.2535	2938560	header( $header = 'Content-type: text/html; charset=UTF-8', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0003	357600	{main}( )	.../index.php:0
2	0.0495	1478384	wfIndexMain( )	.../index.php:46
3	0.0496	1478496	MediaWiki->run( )	.../index.php:50
4	0.0496	1478496	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2534	2921792	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2538	2938480	WebResponse->header( $string = 'Content-language: en', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2826
7	0.2538	2938480	header( $header = 'Content-language: en', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0003	357600	{main}( )	.../index.php:0
2	0.0495	1478384	wfIndexMain( )	.../index.php:46
3	0.0496	1478496	MediaWiki->run( )	.../index.php:50
4	0.0496	1478496	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2534	2921792	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.3562	3720720	OutputPage->sendCacheControl( )	.../OutputPage.php:2891
7	0.3563	3721736	WebResponse->header( $string = 'Vary: Accept-Encoding, Cookie', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2691
8	0.3563	3721736	header( $header = 'Vary: Accept-Encoding, Cookie', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0003	357600	{main}( )	.../index.php:0
2	0.0495	1478384	wfIndexMain( )	.../index.php:46
3	0.0496	1478496	MediaWiki->run( )	.../index.php:50
4	0.0496	1478496	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2534	2921792	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.3562	3720720	OutputPage->sendCacheControl( )	.../OutputPage.php:2891
7	0.3566	3738128	WebResponse->header( $string = 'Expires: Thu, 01 Jan 1970 00:00:00 GMT', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2728
8	0.3566	3738128	header( $header = 'Expires: Thu, 01 Jan 1970 00:00:00 GMT', $replace = TRUE )	.../WebResponse.php:75

Graduate Logic Seminar

Contents

Spring 2018

January 29, Organizational meeting

February 5, Uri Andrews

February 12, James Hanson

February 19, Noah Schweber

February 26, Patrick Nicodemus

March 5, Tamvana Makulumi

March 12, Dan Turetsky (University of Notre Dame)

March 19, Ethan McCarthy

April 2, Wil Cocke

April 9, Tejas Bhojraj

April 16, Iván Ongay-Valverde

April 23, Ethan McCarthy (Thesis Defense) Start 3:45 Room B231

April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde

Fall 2017

September 11, Organizational meeting

September 18, Noah Schweber

September 25, Noah Schweber

October 2, James Hanson

October 9, James Hanson

October 23, Tamvana Makulumi

October 30, Iván Ongay-Valverde

November 6, Wil Cocke

November 13, Steffen Lempp

November 20, Ethan McCarthy

December 4, Tejas Bhojraj

December 11, Grigory Terlov

Previous Years

Navigation menu

Graduate Logic Seminar

Spring 2018

January 29, Organizational meeting

February 5, Uri Andrews

February 12, James Hanson

February 19, Noah Schweber

February 26, Patrick Nicodemus

March 5, Tamvana Makulumi

March 12, Dan Turetsky (University of Notre Dame)

March 19, Ethan McCarthy

April 2, Wil Cocke

April 9, Tejas Bhojraj

April 16, Iván Ongay-Valverde

April 23, Ethan McCarthy (Thesis Defense) Start 3:45 Room B231

April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde

Fall 2017

September 11, Organizational meeting

September 18, Noah Schweber

September 25, Noah Schweber

October 2, James Hanson

October 9, James Hanson

October 23, Tamvana Makulumi

October 30, Iván Ongay-Valverde

November 6, Wil Cocke

November 13, Steffen Lempp

November 20, Ethan McCarthy

December 4, Tejas Bhojraj

December 11, Grigory Terlov

Previous Years

Navigation menu

Search