Graduate Logic Seminar: Difference between revisions

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The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly 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:''' Mondays 3:30-4:30 PM
* '''Where:''' Van Vleck B223.
* '''Where:''' Van Vleck B211
* '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]
* '''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]-->


==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 [mailto:jmiller@math.wisc.edu Joe Miller].


== Fall 2019 - Tentative schedule ==
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1uRSaI1edJ5sepz57NV07ohIfBSKL9FgkvJvMAewk1ms/edit?usp=sharing Sign up here.]


=== September 5 - Organizational meeting ===
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


=== September 9 - No seminar ===


=== September 16 - Daniel Belin ===
==='''September 8 - Organizational Meeting'''===
Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic


Abstract: Lachlan, in a result later refined and clarified by Odifreddi, proved in 1970 that initial segments of the m-degrees can be embedded as an upper semilattice formed as the limit of finite distributive lattices. This allows us to show that the many-one degrees codes satisfiability in second-order arithmetic, due to a later result of Nerode and Shore. We will take a journey through Lachlan's rather complicated construction which sheds a great deal of light on the order-theoretic properties of many-one reducibility.
We will meet to arrange the schedule


=== September 23 - Daniel Belin ===
==='''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: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
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.


=== September 30 - Josiah Jacobsen-Grocott ===
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.


Title: Scott Rank of Computable Models
==='''September 22 - Dan Turetsky'''  ===


Abstract: Infinatary logic extends the notions of first order logic by allowing infinite formulas. Scott's Isomorphism Theorem states that any countable structure can be characterized up to isomorphism by a single countable sentence. Closely related to the complexity of this sentence is what is known as the Scott Rank of the structure. In this talk we restrict our attention to computable models and look at an upper bound on the Scott Rank of such structures.
==='''September 29 - Dan Turetsky'''  ===
==='''October 6 - Dhruv Kulshreshtha'''  ===


=== October 7 - Josiah Jacobsen-Grocott ===
=== '''October 13 - Chiara Travesset''' ===


Title: Scott Rank of Computable Codels - Continued
==='''October 20 -''' ===


=== October 14 - Tejas Bhojraj ===
=== '''October 27 - Yiqing Wang''' ===


Title: Solovay and Schnorr randomness for infinite sequences of qubits.
=== '''November 3 - Logan Heath''' ===


Abstract : We define Solovay and Schnorr randomness in the quantum setting. We then prove quantum versions of the law of large numbers and of the Shannon McMillan Breiman theorem (only for the iid case) for quantum Schnorr randoms.
==='''November 10 -'''  ===


=== October 23 - Tejas Bhojraj ===
==='''November 17 - Hongyu Zhu'''  ===


Title: Solovay and Schnorr randomness for infinite sequences of qubits - continued
==='''November 24 - Taeyoung Em'''  ===


Unusual time and place: Wednesday October 23, 4:30pm, Van Vleck B321.
==='''December 1 - Lucas Duckworth'''  ===


=== October 28 - Two short talks ===
==='''December 8 -'''  ===


'''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
== Previous Years==
 
In 1985, Avraham, Rubin and Shelah published an article where they introduced different coloring axioms. The weakest of them, the Semi-Open Coloring Axiom (SOCA), states that given an uncountable second countable metric space, $E$, and $W\subseteq E^{\dagger}:=E\times E\setminus \{(x, x) :x \in E\}$ open and symmetric, there is an uncountable subset $H\subseteq E$ such that either $H^{\dagger}\subseteq W$ or $H^{\dagger}\cap W=\emptyset$. We say that $W$ is an open coloring and $H$ is a homogeneous subset of $E$. This statement contradicts CH but, as shown also by Avraham, Rubin and Shelah, it is compatible with the continuum taking any other size. This classic paper leaves some questions open (either in an implicit or an explicit way):
 
- Is the axiom weaker if we demand that $W$ is clopen?
- If the continuum is bigger than $\aleph_2$, can we ask that $H$ has the same size as $E$?
- Can we expand this axiom to spaces that are not second countable and metric?
 
These questions lead to different versions of SOCA. In this talk, we will analyze how they relate to the original axiom.
 
'''James Earnest Hanson'''
 
TBA
 
=== November 4 - Two short talks ===
 
Manlio Valenti and Patrick Nicodemus
 
=== November 11 - Manlio Valenti I ===
 
=== November 18 - Manlio Valenti II ===
 
=== November 25 - Two short talks ===
Speakers TBD
 
=== December 2 - Iván Ongay Valverde I ===
 
=== December 9 - Iván Ongay Valverde II ===
 
==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 15:17, 16 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

September 29 - Dan Turetsky

October 6 - Dhruv Kulshreshtha

October 13 - Chiara Travesset

October 20 -

October 27 - Yiqing Wang

November 3 - Logan Heath

November 10 -

November 17 - Hongyu Zhu

November 24 - Taeyoung Em

December 1 - Lucas Duckworth

December 8 -

Previous Years

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

Retrieved from "https://wiki.math.wisc.edu/index.php?title=Graduate_Logic_Seminar&oldid=29099"