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| 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. | | The Graduate Logic Seminar is an informal space where graduate students and professors present topics related to logic which are not necessarily original or completed work. This is a space focused principally on practicing presentation skills or learning materials that are not usually presented in a class. |
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| * '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced). | | * '''When:''' Mondays 3:30-4:30 PM |
| * '''Where:''' Van Vleck B235 (unless otherwise announced). | | * '''Where:''' Van Vleck B211 |
| * '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava] | | * '''Organizer:''' Joseph Miller |
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| Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.
| | The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact the organizers. |
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| == Spring 2018 ==
| | <!--Sign up for the graduate logic seminar mailing list: [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu]--> |
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| === January 29, Organizational meeting === | | ==Fall 2025== |
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| This day we decided the schedule for the semester.
| | The seminar will be run as a 1-credit seminar Math 975. In Fall 2025 students will present a logic topic of their choice (it could be original work, but does not have to be). If you are not enrolled but would like to audit it, please contact [mailto:jmiller@math.wisc.edu Joe Miller]. |
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| === February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===
| | Presentation Schedule: [https://docs.google.com/spreadsheets/d/1uRSaI1edJ5sepz57NV07ohIfBSKL9FgkvJvMAewk1ms/edit?usp=sharing Sign up here.] |
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| Title: Building Models of Strongly Minimal Theories - Part 1
| | <!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)--> |
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| 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
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| 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
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| the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute
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| copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.
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| === February 12, James Hanson === | | ==='''September 8 - Organizational Meeting'''=== |
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| Title: Finding Definable Sets in Continuous Logic
| | We will meet to arrange the schedule |
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| Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic
| | ==='''September 15 - Karthik Ravishankar: Contrasting the halves of an Ahmad pair''' === |
| would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a
| | Abstract: We study Ahmad pairs in the $\Sigma^0_2$ enumeration degrees. We say $(A,B)$ form an Ahmad pair if $A \not \leq_e B$ and every $Z <_e A$ satisfies $Z \leq_e B$. Ahmad pairs have recently drawn interest as they are a key obstacle in solving the $\forall\exists$ theory of the local structure. |
| superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,
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| omega-categorical, and other small theories.
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| === February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
| | In this talk we characterize the left halves of an Ahmad pair as precisely the low$_3$ and join irreducible degrees. We also show that right halves cannot be low$_3$. This is a natural separation between the two halves and is a significant strengthening of previous work. |
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| Title: Proper forcing
| | We then define a hierarchy of join irreducibility notions using which we characterize the left halves of Ahmad $n$-pairs as those that are low$_3$ and $n$-join irreducible. This allows us to extend and clarify previous work to show that for any $n$ there is a set $A$ which is the left half of an Ahmad $n$-pair but not of an Ahmad $(n+1)$-pair. |
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| Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly. | | === '''September 22 - Dan Turetsky: An introduction to the method of true stages. Part 1.''' === |
| Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)
| | Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory. |
| were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is
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| proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and
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| sketch some applications.
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| === February 26, Patrick Nicodemus === | | === '''September 29 - Dan Turetsky: An introduction to the method of true stages. Part 3.''' === |
| | Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory. |
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| Title: A survey of computable and constructive mathematics in economic history
| | ==='''October 6 - Dhruv Kulshreshtha''' === |
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| === March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] === | | === '''October 13 - Chiara Travesset''' === |
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| Title: Convexly Orderable Groups
| | ==='''October 20 -''' === |
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| === March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) === | | === '''October 27 - Yiqing Wang''' === |
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| Title: Structural Jump
| | === '''November 3 - Logan Heath''' === |
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| === March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] === | | ==='''November 10 - Antonio Nakid Cordero''' === |
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| Title: Networks and degrees of points in non-second countable spaces
| | ==='''November 17 - Hongyu Zhu''' === |
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| === April 2, Wil Cocke === | | ==='''November 24 - Taeyoung Em''' === |
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| Title: Characterizing Finite Nilpotent Groups via Word Maps
| | ==='''December 1 - Lucas Duckworth''' === |
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| 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.
| | ==='''December 8 - John Spoerl''' === |
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| === April 9, Tejas Bhojraj === | | == Previous Years== |
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| Title: Quantum Randomness
| | The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]]. |
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| 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.
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| === April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===
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| Title: What can we say about sets made by the union of Turing equivalence classes?
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| 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?
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| 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.
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| This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).
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| === April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) ===
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| Title: Cototal enumeration degrees and their applications to effective mathematics (thesis defense)
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| 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.
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| 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>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.
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| === April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===
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| Title: TBA
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| Abstract: TBA
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| == Fall 2017 ==
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| === September 11, Organizational meeting ===
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| This day we decided the schedule for the semester.
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| === September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
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| Title: The Kunen inconsistency
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| Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's
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| theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the
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| whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a
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| nontrivial elementary embedding from V into some inner model M.
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| There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the
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| inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The
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| critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's
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| thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.
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| I'll present this argument, and talk a bit about the role of choice.
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| === September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
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| Title: Hindman's theorem via ultrafilters
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| 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.
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| === October 2, James Hanson ===
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| Title: The Gromov-Hausdorff metric on type space in continuous logic
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| 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.
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| === October 9, James Hanson ===
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| Title: Morley rank and stability in continuous logic
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| 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
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| > 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.
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| === October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===
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| Title: Boxy sets in ordered convexly-orderable structures.
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| === October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===
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| Title: Dancing SCCA and other Coloring Axioms
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| 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.
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| === November 6, Wil Cocke ===
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| Title: Two new characterizations of nilpotent groups
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| 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.
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| Or...
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| Title: Centralizing Propagating Properties of Groups
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| 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.
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| === November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===
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| Title: The computational complexity of properties of finitely presented groups
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| Abstract: I will survey index set complexity results on finitely presented groups.
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| === November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===
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| Title: Strong Difference Randomness
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| 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.
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| === December 4, Tejas Bhojraj ===
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| Title: Quantum Algorithmic Randomness
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| 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.
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| === December 11, Grigory Terlov ===
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| Title: The Logic of Erdős–Rényi Graphs
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| ==Previous Years==
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| The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]]. | |
The Graduate Logic Seminar is an informal space where graduate students and professors present topics related to logic which are not necessarily original or completed work. This is a space focused principally on practicing presentation skills or learning materials that are not usually presented in a class.
- When: Mondays 3:30-4:30 PM
- Where: Van Vleck B211
- Organizer: Joseph Miller
The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact the organizers.
Fall 2025
The seminar will be run as a 1-credit seminar Math 975. In Fall 2025 students will present a logic topic of their choice (it could be original work, but does not have to be). If you are not enrolled but would like to audit it, please contact Joe Miller.
Presentation Schedule: Sign up here.
September 8 - Organizational Meeting
We will meet to arrange the schedule
September 15 - Karthik Ravishankar: Contrasting the halves of an Ahmad pair
Abstract: We study Ahmad pairs in the $\Sigma^0_2$ enumeration degrees. We say $(A,B)$ form an Ahmad pair if $A \not \leq_e B$ and every $Z <_e A$ satisfies $Z \leq_e B$. Ahmad pairs have recently drawn interest as they are a key obstacle in solving the $\forall\exists$ theory of the local structure.
In this talk we characterize the left halves of an Ahmad pair as precisely the low$_3$ and join irreducible degrees. We also show that right halves cannot be low$_3$. This is a natural separation between the two halves and is a significant strengthening of previous work.
We then define a hierarchy of join irreducibility notions using which we characterize the left halves of Ahmad $n$-pairs as those that are low$_3$ and $n$-join irreducible. This allows us to extend and clarify previous work to show that for any $n$ there is a set $A$ which is the left half of an Ahmad $n$-pair but not of an Ahmad $(n+1)$-pair.
September 22 - Dan Turetsky: An introduction to the method of true stages. Part 1.
Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory.
September 29 - Dan Turetsky: An introduction to the method of true stages. Part 3.
Abstract: True stages are a method for organizing complex constructions in computability theory. Over several lectures, I'll explain the method of true stages by working through some examples in computable structure theory. We'll start with some necessary computability background. Time permitting, I may discuss some of the applications of true stages to descriptive set theory.
October 6 - Dhruv Kulshreshtha
October 13 - Chiara Travesset
October 20 -
October 27 - Yiqing Wang
November 3 - Logan Heath
November 10 - Antonio Nakid Cordero
November 17 - Hongyu Zhu
November 24 - Taeyoung Em
December 1 - Lucas Duckworth
December 8 - John Spoerl
Previous Years
The schedule of talks from past semesters can be found here.