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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 B223
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
* '''Organizers:''' [https://uriandrews.netlify.app/ Uri Andrews] and [https://sites.google.com/view/hongyu-zhu/ Hongyu Zhu]


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.


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]


== Fall 2021 - Tentative schedule ==
== Fall 2023 ==


To see what's happening in the Logic qual preparation sessions click [[Logic Qual Prep|here]].
The seminar will be run as a 1-credit seminar Math 975 in Fall 2023. If you are not enrolled but would like to audit it, please contact [mailto:andrews@math.wisc.edu Uri Andrews] and [mailto:hongyu@math.wisc.edu Hongyu Zhu].


== Spring 2021 - Tentative schedule ==
While you are welcome (and encouraged) to present on a topic of your own choice, feel free to ask for help from faculties and/or other graduate students.


=== February 16 3:30PM - Short talk by Sarah Reitzes (University of Chicago) ===
Presentation Schedule: https://docs.google.com/spreadsheets/d/15Qd4EzrrKpn1Ct5tur1P_FDc2czsdAVnUf_pfp65Lb4/edit?usp=sharing


Title: Reduction games over $\mathrm{RCA}_0$
Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)


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.
Possible readings:
* (Elementary) Proof Theory: Chapters 4-7 of <i>[https://projecteuclid.org/ebooks/lecture-notes-in-logic/Aspects-of-Incompleteness/toc/lnl/1235416274 Aspects of Incompleteness]</i> by Per Lindström.
* An invitation to model-theoretic Galois theory.  <i>[https://arxiv.org/abs/0909.4340 On arxiv here.]</i>
* Variations on the Feferman-Vaught Theorem <i>[https://arxiv.org/abs/1812.02905 On arxiv here.]</i>
* Any of several papers on "Turing Computable Embeddings"
* Computability/Model/Set Theory: Consult faculties/students for recommended texts on specific areas.


=== March 23 4:15PM - Steffen Lempp ===
=== September 11 - Organizational Meeting ===


Title: Degree structures and their finite substructures
We will meet to assign speakers to dates.


Abstract: Many problems in mathematics can be viewed as being coded by sets of natural numbers (as indices).
=== '''September 18 - Taeyoung Em''' ===
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).
'''Title:''' Explicit construction of non-quasidetermined game on <math>\mathcal P(2^{\mathbb N})</math> without using A.C. ([https://wiki.math.wisc.edu/images/Gale-Stewart_implies_A.C..pdf Supplement])
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 ===
'''Abstract:''' We will go over briefly some basic information about trees and infinite games. Then we prove the Gale-Stewart Theorem. The proof of the theorem motivates definition of quasistrategy. Then we will briefly introduce Borel determinacy. We will go over how the usage of A.C. makes convenient for us to make a non-quasidetermined or undertermined game. We will give an explicit construction of a non-quasidetermined game on <math>\mathcal P(2^{\mathbb N})</math> without using A.C.


Title: Categorical logic for realizability, part I: Categories and the Yoneda Lemma
=== '''September 25 - Karthik Ravishankar''' ===
'''Title:''' Spectra of structures


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.
'''Abstract:''' One way to measure the complexity of a structure is via its spectrum - the set of Turing degrees of its copies. In this talk, we'll look at the definition and first properties of the spectrum followed by some examples. In particular, we'll show that the non-computable degrees and the hyperimmune degrees form a spectrum while the DNC degrees do not.


[https://hilbert.math.wisc.edu/wiki/images/Cat-slides-1.pdf Link to slides]
<!-- Template


=== April 27 4PM - Alice Vidrine ===
=== '''September 18 - Karthik Ravishankar''' ===
'''Title:''' Lowness for Isomorphism ([https://wiki.math.wisc.edu/images/Karthik_talk.pdf Slides])


Title: Categorical logic for realizability, part II
'''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.


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.
-->


==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 15:05, 23 September 2023

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 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 2023

The seminar will be run as a 1-credit seminar Math 975 in Fall 2023. If you are not enrolled but would like to audit it, please contact Uri Andrews and Hongyu Zhu.

While you are welcome (and encouraged) to present on a topic of your own choice, feel free to ask for help from faculties and/or other graduate students.

Presentation Schedule: https://docs.google.com/spreadsheets/d/15Qd4EzrrKpn1Ct5tur1P_FDc2czsdAVnUf_pfp65Lb4/edit?usp=sharing

Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)

Possible readings:

  • (Elementary) Proof Theory: Chapters 4-7 of Aspects of Incompleteness by Per Lindström.
  • An invitation to model-theoretic Galois theory. On arxiv here.
  • Variations on the Feferman-Vaught Theorem On arxiv here.
  • Any of several papers on "Turing Computable Embeddings"
  • Computability/Model/Set Theory: Consult faculties/students for recommended texts on specific areas.

September 11 - Organizational Meeting

We will meet to assign speakers to dates.

September 18 - Taeyoung Em

Title: Explicit construction of non-quasidetermined game on [math]\displaystyle{ \mathcal P(2^{\mathbb N}) }[/math] without using A.C. (Supplement)

Abstract: We will go over briefly some basic information about trees and infinite games. Then we prove the Gale-Stewart Theorem. The proof of the theorem motivates definition of quasistrategy. Then we will briefly introduce Borel determinacy. We will go over how the usage of A.C. makes convenient for us to make a non-quasidetermined or undertermined game. We will give an explicit construction of a non-quasidetermined game on [math]\displaystyle{ \mathcal P(2^{\mathbb N}) }[/math] without using A.C.

September 25 - Karthik Ravishankar

Title: Spectra of structures

Abstract: One way to measure the complexity of a structure is via its spectrum - the set of Turing degrees of its copies. In this talk, we'll look at the definition and first properties of the spectrum followed by some examples. In particular, we'll show that the non-computable degrees and the hyperimmune degrees form a spectrum while the DNC degrees do not.


Previous Years

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

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