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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: 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.


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: 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 7 - Josiah Jacobsen-Grocott ===
=== '''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.


Title: Scott Rank of Computable Codels - Continued
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 14 - Tejas Bhojraj ===
=== '''October 13 - Chiara Travesset''' ===


Title: Solovay and Schnorr randomness for infinite sequences of qubits.
==='''October 20 -''' ===


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.
=== '''October 27 - Yiqing Wang''' ===


=== October 23 - Tejas Bhojraj ===
=== '''November 3 - Logan Heath''' ===


Title: Solovay and Schnorr randomness for infinite sequences of qubits - continued
==='''November 10 - Antonio Nakid Cordero'''  ===


Unusual time and place: Wednesday October 23, 4:30pm, Van Vleck B321.
==='''November 17 - Hongyu Zhu'''  ===


=== October 28 - Two short talks ===
==='''November 24 - Taeyoung Em'''  ===


'''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
==='''December 1 - Lucas Duckworth''' ===


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):
==='''December 8 - John Spoerl'''  ===


- Is the axiom weaker if we demand that $W$ is clopen?
== Previous Years==
- 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''' - Strongly minimal sets in continuous logic
 
The precise structural understanding of uncountably categorical theories given by the proof of the Baldwin-Lachlan theorem is known to fail in continuous logic in the context of inseparably categorical theories. The primary obstacle is the absence of strongly minimal sets in some inseparably categorical theories. We will develop the concept of strongly minimal sets in continuous logic and discuss some common conditions under which they are present in an $\omega$-stable theory. Finally, we will examine the extent to which we recover a Baldwin-Lachlan style characterization in the presence of strongly minimal sets.
 
=== November 4 - Two short talks ===
 
'''Manlio Valenti''' - The complexity of closed Salem sets (20 minutes version)
 
A central notion in geometric measure theory is the one of Hausdorff dimension. As a consequence of Frostman's lemma, the Hausdorff dimension of a Borel subset A of the Euclidean n-dimensional space can be determined by looking at the behaviour of probability measures with support in A. The possibility to apply methods from Fourier analysis to estimate the Hausdorff dimension gives birth to the notion of Fourier dimension. It is known that, for Borel sets, the Fourier dimension is less than or equal to the Hausdorff dimension. The sets for which the two notions agree are called Salem sets.
In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.
 
'''Patrick Nicodemus''' - TBD
 
=== November 11 - Manlio Valenti ===
 
Title: The complexity of closed Salem sets (full length)
 
Abstract:
A central notion in geometric measure theory is the one of Hausdorff dimension. As a consequence of Frostman's lemma, the Hausdorff dimension of a Borel subset A of the Euclidean n-dimensional space can be determined by looking at the behaviour of probability measures with support in A. The possibility to apply methods from Fourier analysis to estimate the Hausdorff dimension gives birth to the notion of Fourier dimension. It is known that, for Borel sets, the Fourier dimension is less than or equal to the Hausdorff dimension. The sets for which the two notions agree are called Salem sets.
 
In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.
 
=== 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 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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