Difference between revisions of "Graduate Logic Seminar"

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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.
 
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 4p-5p (unless stated otherwise)
+
* '''When:''' Tuesdays 4-5 PM
* '''Where:''' on line (ask for code).
+
* '''Where:''' Van Vleck 901
 
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
 
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
  
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Sign up for the graduate logic seminar mailing list:  join-grad-logic-sem@lists.wisc.edu
 
Sign up for the graduate logic seminar mailing list:  join-grad-logic-sem@lists.wisc.edu
  
== Fall 2020 - Tentative schedule ==
+
== Spring 2022 ==
  
=== September 14 - Josiah Jacobsen-Grocott ===
+
The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.
  
Title: Degrees of points in topological spaces
+
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].
  
Abstract: An overview of some results from Takayuki Kihara, Keng Meng Ng, and Arno Pauly in their paper Enumeration Degrees and Non-Metrizable Topology. We will look at a range of topological spaces and the corresponding classes in the enumeration degrees as well as ways in which we can distinguish the type of classes using the separation axioms.
+
=== January 25 - organizational meeting ===
  
=== September 28 - James Hanson ===
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We will meet to assign speakers to dates.
  
Title: The Semilattice of Definable Sets in Continuous Logic
+
=== February 1 - Steffen Lempp ===
  
Abstract: After an analysis-free exposition of definable sets in continuous logic, we will present a fun, illustrated proof that any finite bounded lattice can be the poset of definable subsets of $S_1(T)$ for a continuous theory $T$.
+
I will give an overview of the topics we will cover:
  
=== October 5 - Tejas Bhojraj from 3:30PM-4:00PM ===
+
1. the base theory PA^- and the induction and bounding axioms for Sigma_n-formulas, and how they relate to each other,
  
Title: A Levin-Schnorr type result for Weak Solovay random states.
+
2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),
  
Abstract: We look at the initial-segment complexity of Weak Solovay quantum random states using MK, a prefix-free version of quantum Kolmogorov complexity. The statement of our result is similar to the Levin-Schnorr theorem in classical algorithmic randomness.
+
3. the Grzegorczyk hierarchy of fast-growing functions,
  
=== November 9 - Karthik Ravishankar ===
+
4. end extensions and cofinal extensions,
  
Title: Elementary submodels in infinite combinatorics
+
5. recursive saturation and resplendency,
  
Abstract: The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. In the first part of the talk, we quickly cover the basic concepts involved for proving results using elementary submodels, and move on to provide two examples of application of the technique to prove two popular results from set theory: The Delta System lemma and the Fodors Pressing down lemma . We provide both the classical proof as well as a proof using elementary submodels to contrast the two approaches.
+
6. standard systems and coded types,
  
=== November 16 - Karthik Ravishankar ===
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7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and
  
Title: Elementary submodels in infinite combinatorics, part II
+
8. Gaifman's theorem that every model of PA has a minimal elementary end extension.
  
Abstract: In the second part of the talk, we give a proof Fodors Pressing down lemma, along with an overview of the slightly larger proof of the Nash Williams theorem which states that a graph is decomposable as a disjoint union of cycles if and only if it has no odd cut.
+
I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much
 +
background.
  
=== Tuesday, November 24 - Tonicha Crook (Swansea University) from 9:00AM-10:00AM ===
+
=== February 8 - Karthik Ravishankar ===
  
Title: The Weihrauch Degree of Finding Nash Equilibria in Multiplayer Games
+
Title: Collection axioms
  
Abstract: Is there an algorithm that takes a game in normal form as input, and outputs a Nash equilibrium? If the payoffs are integers, the answer is yes, and a lot of work has been done in its computational complexity. If the payoffs are permitted to be real numbers, the answer is no, for continuity reasons. It is worthwhile to investigate the precise degree of non-computability (the Weihrauch degree), since knowing the degree entails what other approaches are available (eg, is there a randomized algorithm with positive success change?). The two player case has already been fully classified, but the multiplayer case remains open and is addressed here. As well as some insight into finding the roots of polynomials, which is essential in our research. An in-depth introduction to Weihrauch Reducibility will be included in the presentation, along with a small introduction to Game Theory.
+
We will discuss parts 1 and 2 of Wong's notes.
  
=== November 30 - Yvette Ren ===
+
=== February 15 - Karthik Ravishankar, Yunting Zhang ===
  
Title: Enumeration Degrees and Topology
+
Title: Collection axioms/The Weak König Lemma
  
Abstract: I will introduce three classes of enumeration degrees: co-dcea degrees, telegraph-cototal degrees and cylinder-cototal degrees and discuss the relations between each other. Selected results from Kihara, Pauly, and Ng’s paper ''Enumeration Degrees and Non-Metrizable Topology'' and their alternative proofs will be presented.
+
Karthik will finish part 2 of Wong's notes. Then Yunting will start on part 3 of Wong's notes.
  
==Previous Years==
+
=== 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 [[Graduate Logic Seminar, previous semesters|here]].
 
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].

Latest revision as of 12:44, 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.