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:''' Tuesdays 4-5 PM
+
* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' Van Vleck 901
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* '''Where:''' Van Vleck B139
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
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* '''Organizers:''' Karthik Ravishankar and [https://sites.google.com/wisc.edu/antonio Antonio Nakid Cordero]
  
 
The talk schedule is arranged 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.
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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
  
== Spring 2022 ==
+
== Fall 2022 ==
  
The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.
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=== September 12 - Organizational Meeting ===
 
 
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].
 
 
 
=== January 25 - organizational meeting ===
 
  
 
We will meet to assign speakers to dates.
 
We will meet to assign speakers to dates.
  
=== February 1 - Steffen Lempp ===
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=== '''September 19 - Karthik Ravishankar''' ===
 
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'''Title:''' Lowness for Isomorphism
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
+
'''Abstract:''' A Turing degree is said to be low for isomorphism if it can only compute an isomorphism between computable structures only when a computable isomorphism already exists. In this talk, we show that the measure of the class of low for isomorphism sets in Cantor space is 0 and that no Martin Lof random is low for isomorphism.
  
We will finish part 4 of Wong's notes.
+
=== '''September 26 - Antonio Nakid Cordero''' ===
 +
'''Title:''' When Models became Polish: an introduction to the Topological Vaught Conjecture
  
=== April 5 - Antonio Nákid Cordero ===
+
'''Abstract:''' Vaught's Conjecture, originally asked by Vaught in 1961, is one of the most (in)famous open problems in mathematical logic. The conjecture is that a complete theory on a countable language must either have countably-many or continuum-many non-isomorphic models. In this talk, we will discuss some of the main ideas that surround this conjecture, with special emphasis on a topological generalization in terms of the continuous actions of Polish groups.
  
Title: Semiregular cuts
+
=== '''October 3 - Yunting Zhang''' ===
  
We will start on part 5 of Wong's notes.
+
=== '''October 10 - Yuxiao Fu''' ===
  
=== April 12 - Antonio Nákid Cordero/Alice Vidrine ===
+
=== '''October 17 - Alice Vidrine''' ===
  
Title: Semiregular cuts/End and cofinal extensions
+
=== '''October 24 - Hongyu Zhu''' ===
  
We will finish part 5 of Wong's notes and then start on part 6.
+
=== '''October 31 - Break for Halloween''' ===
  
=== April 19 - Alice Vidrine ===
+
=== '''November 7 - John Spoerl''' ===
  
Title: End and cofinal extensions
+
=== '''November 14 - Josiah Jacobsen-Grocott''' ===
  
We will finish part 6 of Wong's notes.
+
=== '''November 21 - Karthik Ravishankar''' ===
  
=== April 26 - Josiah Jacobsen-Grocott ===
+
=== '''November 28 - Logan Heath''' ===
  
Title: Recursive saturation
+
=== '''December 5 - Logan Heath''' ===
  
We will start on part 7 of Wong's notes.
+
=== '''December 12 - TBA''' ===
  
 
== Previous Years ==
 
== 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 01:20, 26 September 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: Mondays 3:30-4:30 PM
  • Where: Van Vleck B139
  • Organizers: Karthik Ravishankar and Antonio Nakid Cordero

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

Fall 2022

September 12 - Organizational Meeting

We will meet to assign speakers to dates.

September 19 - Karthik Ravishankar

Title: Lowness for Isomorphism

Abstract: A Turing degree is said to be low for isomorphism if it can only compute an isomorphism between computable structures only when a computable isomorphism already exists. In this talk, we show that the measure of the class of low for isomorphism sets in Cantor space is 0 and that no Martin Lof random is low for isomorphism.

September 26 - Antonio Nakid Cordero

Title: When Models became Polish: an introduction to the Topological Vaught Conjecture

Abstract: Vaught's Conjecture, originally asked by Vaught in 1961, is one of the most (in)famous open problems in mathematical logic. The conjecture is that a complete theory on a countable language must either have countably-many or continuum-many non-isomorphic models. In this talk, we will discuss some of the main ideas that surround this conjecture, with special emphasis on a topological generalization in terms of the continuous actions of Polish groups.

October 3 - Yunting Zhang

October 10 - Yuxiao Fu

October 17 - Alice Vidrine

October 24 - Hongyu Zhu

October 31 - Break for Halloween

November 7 - John Spoerl

November 14 - Josiah Jacobsen-Grocott

November 21 - Karthik Ravishankar

November 28 - Logan Heath

December 5 - Logan Heath

December 12 - TBA

Previous Years

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