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
+
* '''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
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=== 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,
  
==Previous Years==
+
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.
 +
 
 +
== 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]].

Revision as of 19:06, 25 January 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.

Previous Years

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