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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.


* '''When:''' Fridays, 3:30 PM - 4:30 PM (unless otherwise announced).
* '''When:''' Tuesdays 4-5 PM
* '''Where:''' Van Vleck B115 (unless otherwise announced).
* '''Where:''' Van Vleck 901
* '''Organizers:''' [https://www.math.wisc.edu/~schweber/ Noah Schweber]
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]


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 one of the organizers.


== Spring 2018 ==
Sign up for the graduate logic seminar mailing list:  join-grad-logic-sem@lists.wisc.edu


=== January 29, Organizational meeting ===
== Spring 2022 ==


This day we decided the schedule for the semester.
The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.


=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===
We plan to cover the first 9 parts of [https://blog.nus.edu.sg/matwong/teach/modelarith/ Tin Lok Wong's notes], as well as a few other relevant topics which are not covered in the notes:
* Properness of the induction/bounding hierarchy (chapter 10 of Models of Peano Arithmetic by Kaye is a good source)
* Tennenbaum's theorem (this is a quick consequence of the main theorem of part 4, so it should be combined with part 4 or part 5)
* Other facts found in chapter 1 of [http://homepages.math.uic.edu/~marker/marker-thesis.pdf David Marker's thesis].


Title: Building Models of Strongly Minimal Theories - Part 1
=== January 25 - organizational meeting ===


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
We will meet to assign speakers to dates.
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 ===
=== February 1 - Steffen Lempp ===


Title: Finding Definable Sets in Continuous Logic
I will give an overview of the topics we will cover:  


Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic
1. the base theory PA^- and the induction and bounding axioms for Sigma_n-formulas, and how they relate to each other,
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, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),


Title: Proper forcing
3. the Grzegorczyk hierarchy of fast-growing functions,


Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.
4. end extensions and cofinal extensions,
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 ===
5. recursive saturation and resplendency,


Title: A survey of computable and constructive mathematics in economic history
6. standard systems and coded types,


=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===
7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and


Title: Convexly Orderable Groups
8. Gaifman's theorem that every model of PA has a minimal elementary end extension.


=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===
I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much
background.


Title: Structural Jump
=== February 8 - Karthik Ravishankar ===


=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===
Title: Collection axioms


Title: Networks and degrees of points in non-second countable spaces
We will discuss parts 1 and 2 of Wong's notes.


=== April 2, Wil Cocke ===
=== February 15 - Karthik Ravishankar, Yunting Zhang ===


Title: Characterizing Finite Nilpotent Groups via Word Maps
Title: Collection axioms/The Weak König Lemma


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.
Karthik will finish part 2 of Wong's notes. Then Yunting will start on part 3 of Wong's notes.


=== April 9, Tejas Bhojraj ===
=== February 22 - Yunting Zhang ===


Title: Quantum Randomness
Title: The Weak König Lemma


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.  
We will finish part 3 of Wong's notes.


=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===
=== March 22 - Ang Li ===


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


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?
We will discuss part 4 of Wong's notes.


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.
=== March 29 - Ang Li ===


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


=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===
We will finish part 4 of Wong's notes.


Title: Cototal enumeration degrees and their applications to effective mathematics
=== April 5 - Antonio Nákid Cordero ===


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.
Title: Semiregular cuts


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.
We will start on part 5 of Wong's notes.


=== April 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde]===
=== April 12 - Antonio Nákid Cordero/Alice Vidrine ===


Title: Definibility of the Frobenius orbits and an application to sets of rational distances.
Title: Semiregular cuts/End and cofinal extensions


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).
We will finish part 5 of Wong's notes and then start on part 6.


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.
=== April 19 - Alice Vidrine ===


== Fall 2017 ==
Title: End and cofinal extensions


=== September 11, Organizational meeting ===
We will finish part 6 of Wong's notes.


This day we decided the schedule for the semester.
=== May 3 - No seminar today ===


=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
== Previous Years ==


Title: The Kunen inconsistency
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].
 
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, [https://sites.google.com/a/wisc.edu/schweber/ 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, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===
 
Title: Boxy sets in ordered convexly-orderable structures.
 
=== October 30, [http://www.math.wisc.edu/~ongay/ 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, [https://www.math.wisc.edu/~lempp/ 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, [http://www.math.wisc.edu/~mccarthy/ 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 [[Logic Graduate Seminar, previous semesters|here]].

Revision as of 17:44, 2 May 2022

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: Tuesdays 4-5 PM
  • Where: Van Vleck 901
  • Organizers: Jun Le Goh

The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact one of the organizers.

Sign up for the graduate logic seminar mailing list: join-grad-logic-sem@lists.wisc.edu

Spring 2022

The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.

We plan to cover the first 9 parts of Tin Lok Wong's notes, as well as a few other relevant topics which are not covered in the notes:

  • Properness of the induction/bounding hierarchy (chapter 10 of Models of Peano Arithmetic by Kaye is a good source)
  • Tennenbaum's theorem (this is a quick consequence of the main theorem of part 4, so it should be combined with part 4 or part 5)
  • Other facts found in chapter 1 of David Marker's thesis.

January 25 - organizational meeting

We will meet to assign speakers to dates.

February 1 - Steffen Lempp

I will give an overview of the topics we will cover:

1. the base theory PA^- and the induction and bounding axioms for Sigma_n-formulas, and how they relate to each other,

2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),

3. the Grzegorczyk hierarchy of fast-growing functions,

4. end extensions and cofinal extensions,

5. recursive saturation and resplendency,

6. standard systems and coded types,

7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and

8. Gaifman's theorem that every model of PA has a minimal elementary end extension.

I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much background.

February 8 - Karthik Ravishankar

Title: Collection axioms

We will discuss parts 1 and 2 of Wong's notes.

February 15 - Karthik Ravishankar, Yunting Zhang

Title: Collection axioms/The Weak König Lemma

Karthik will finish part 2 of Wong's notes. Then Yunting will start on part 3 of Wong's notes.

February 22 - Yunting Zhang

Title: The Weak König Lemma

We will finish part 3 of Wong's notes.

March 22 - Ang Li

Title: The Arithmetized Completeness Theorem

We will discuss part 4 of Wong's notes.

March 29 - Ang Li

Title: The Arithmetized Completeness Theorem

We will finish part 4 of Wong's notes.

April 5 - Antonio Nákid Cordero

Title: Semiregular cuts

We will start on part 5 of Wong's notes.

April 12 - Antonio Nákid Cordero/Alice Vidrine

Title: Semiregular cuts/End and cofinal extensions

We will finish part 5 of Wong's notes and then start on part 6.

April 19 - Alice Vidrine

Title: End and cofinal extensions

We will finish part 6 of Wong's notes.

May 3 - No seminar today

Previous Years

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

Retrieved from "https://wiki.math.wisc.edu/index.php?title=Graduate_Logic_Seminar&oldid=23203"