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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:''' TBA
* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' on line (ask for code).
* '''Where:''' Van Vleck B211
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
* '''Organizer:''' Joseph Miller


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 the organizers.


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:  [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu]-->


== Spring 2021 - Tentative schedule ==
==Fall 2025==


=== February 16 3:30PM - Short talk by Sarah Reitzes (University of Chicago) ===
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].


Title: Reduction games over $\mathrm{RCA}_0$
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1uRSaI1edJ5sepz57NV07ohIfBSKL9FgkvJvMAewk1ms/edit?usp=sharing Sign up here.]


Abstract: In this talk, I will discuss joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt. Our work centers on the characterization of problems P and Q such that P $\leq_{\omega}$ Q, as well as problems P and Q such that $\mathrm{RCA}_0 \vdash$ Q $\to$ P, in terms of winning strategies in certain games. These characterizations were originally introduced by Hirschfeldt and Jockusch. I will discuss extensions and generalizations of these characterizations, including a certain notion of compactness that allows us, for strategies satisfying particular conditions, to bound the number of moves it takes to win. This bound is independent of the instance of the problem P being considered. This allows us to develop the idea of Weihrauch and generalized Weihrauch reduction over some base theory. Here, we will focus on the base theory $\mathrm{RCA}_0$. In this talk, I will explore these notions of reduction among various principles, including bounding and induction principles.
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


=== March 23 4:15PM - Steffen Lempp ===


Title: Degree structures and their finite substructures
==='''September 8 - Organizational Meeting'''===


Abstract: Many problems in mathematics can be viewed as being coded by sets of natural numbers (as indices).
We will meet to arrange the schedule
One can then define the relative computability of sets of natural numbers in various ways, each leading to a precise notion of “degree” of a problem (or set).
In each case, these degrees form partial orders, which can be studied as algebraic structures.
The study of their finite substructures leads to a better understanding of the partial order as a whole.


=== March 30 4PM - Alice Vidrine ===
==='''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.


Title: Categorical logic for realizability, part I: Categories and the Yoneda Lemma
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.


Abstract: An interesting strand of modern research on realizability--a semantics for non-classical logic based on a notion of computation--uses the language of toposes and Grothendieck fibrations to study mathematical universes whose internal notion of truth is similarly structured by computation. The purpose of this talk is to establish the basic notions of category theory required to understand the tools of categorical logic developed in the sequel, with the end goal of understanding the realizability toposes developed by Hyland, Johnstone, and Pitts. The talk will cover the definitions of category, functor, natural transformation, adjunctions, and limits/colimits, with a heavy emphasis on the ubiquitous notion of representability.
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.


[https://hilbert.math.wisc.edu/wiki/images/Cat-slides-1.pdf Link to slides]
=== '''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.


=== April 27 4PM - Alice Vidrine ===
=== '''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.


Title: Categorical logic for realizability, part II
=== '''October 6 - Dhruv Kulshreshtha: Classification by countable structures''' ===
Abstract: Self-homeomorphisms of the interval [0,1] can be classified up to conjugacy by using certain countable structures as invariants. On the other hand, Hjorth showed that there is no definable way to classify self-homeomorphisms of the square [0,1]^2 in this manner.


Abstract: Realizability is an approach to semantics for non-classical logic that interprets propositions by sets of abstract computational data. One modern approach to realizability makes heavy use of the notion of a topos, a type of category that behaves like a universe of non-standard sets. In preparation for introducing realizability toposes, the present talk will be a brisk introduction to the notion of a topos, with an emphasis on their logical aspects. In particular, we will look at the notion of a subobject classifier and the internal logic to which it gives rise.
In this talk, upon making these notions precise, we briefly discuss the machinery that is used to prove the aforementioned negative result. We then take a step towards studying the more general interplay between dimension and classifiability by arguing that homeomorphisms of the Sierpiński carpet, the one-dimensional universal plane curve, also cannot be classified in this manner. This result is based on joint work with Aristotelis Panagiotopoulos.


==Previous Years==
=== '''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 [[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 19:04, 29 September 2025

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: Classification by countable structures

Abstract: Self-homeomorphisms of the interval [0,1] can be classified up to conjugacy by using certain countable structures as invariants. On the other hand, Hjorth showed that there is no definable way to classify self-homeomorphisms of the square [0,1]^2 in this manner.

In this talk, upon making these notions precise, we briefly discuss the machinery that is used to prove the aforementioned negative result. We then take a step towards studying the more general interplay between dimension and classifiability by arguing that homeomorphisms of the Sierpiński carpet, the one-dimensional universal plane curve, also cannot be classified in this manner. This result is based on joint work with Aristotelis Panagiotopoulos.

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.

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