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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 B215.
* '''Where:''' Van Vleck B235
* '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]
* '''Organizer:''' Mariya Soskova


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 2020 - Tentative schedule ==
== Spring 2025 ==


=== January 28 - Talk by visitor - No seminar ===
The seminar will be run as a 1-credit seminar Math 975. In Spring 2025, we will finish last semester's topic on Higher Computability Theory.Once we are done 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:soskova@wisc.edu Mariya Soskova].
=== February 3 - Talk by visitor - No seminar ===
=== February 10 - No seminar (speaker was sick) ===


=== February 17 - James Hanson ===
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1uRSaI1edJ5sepz57NV07ohIfBSKL9FgkvJvMAewk1ms/edit?usp=sharing Sign up here.]


Title: The Topology of Definable Sets in Continuous Logic
Notes on Higher Computability Theory: [https://uwmadison.box.com/s/j3xftdj1i70d4lblxhzswhg9e25ajcpq Download the notes here.] You will need your UW-login. Please, do not distribute these notes without permission from the author.


Abstract: We will look at the topology of certain special subsets of type spaces in continuous logic, such as definable sets. In the process we will characterize those type spaces which have 'enough definable sets' and look at some counterexamples to things which would have been nice.
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


=== February 24 - Two short talks - Tejas Bhojraj and Josiah Jacobsen-Grocott ===
=== '''January 27 - Organizational Meeting and Sapir Ben-Shahar''' ===


'''Tejas Bhojraj''' - Quantum Kolmogorov Complexity.
Mariya Soskova will call for volunteers to sign up for presentations.  


Abstract: We define a notion of quantum Kolmogorov complexity and relate it to quantum Solovay and quantum Schnorr randomness.
Sapir Ben-Shahar will wrap up Section 5.1


'''Josiah Jacobsen-Grocott''' - A Characterization of Strongly $\eta$-Representable Degrees.
=== '''February 3 - Taeyoung Em''' ===


Abstract:
Taeyoung Em will present Section 5.3.  
$\eta$-representations are a way of coding sets in computable linear orders that were first
introduced by Fellner in his PhD thesis. Limitwise monotonic functions have been used to
characterize the sets with $\eta$-representations as well as the sets with subclasses of
$\eta$-representations except for the case of sets with strong $\eta$-representations, the only
class where the order type of the representation is unique.


We introduce the notion of a connected approximation of a set, a variation on $\Sigma^0_2$
=== '''February 10 - Hongyu Zhu''' ===
approximations. We use connected approximations to
give a characterization of the degrees with strong $\eta$-representations as well new
characterizations of the subclasses of $\eta$-representations with known characterizations.


=== March 2 - Patrick Nicodemus ===
Hongyu Zhu will present Section 5.3


Title: A Sheaf-theoretic generalization of Los's theorem
=== '''February 17 - Karthik Ravishankar''' ===


Abstract: Sheaf theory deals in part with the behavior of functions on a small open neighborhood of a point. As one chooses smaller and smaller open neighborhoods around a point, one gets closer to the limit - the "germ" of the function of the point. The relationship between the "finite approximation" (the function's behavior on a small, but not infinitesimal, neighborhood) and the "limit" (its infinitesimal behavior) is akin to the concept of reasoning with finite approximations that underlies forcing. Indeed, there is a natural forcing language that arises in sheaf theory - this is somewhat unsurprising as at a purely formal level, a sheaf is almost identical as a data structure to a Kripke model. We will demonstrate the applicability of this forcing language by giving a Los's theorem for sheaves of models.
'''Title:''' Strong minimal covers and the cupping property


=== March 9 - Noah Schweber ===
'''Abstract:''' A longstanding question in degree theory has been whether every minimal Turing degree has a strong minimal cover. Meanwhile a strong example of degrees without SMC's are those which have the cupping property. It is known that PA degrees have the cupping property, as do degrees with a certain amount of escaping power. On the other hand, it is known that being weak in the sense of being non DNC and Hyperimmune-free lets you have a SMC. Degrees with the cupping property are closed upwards while it is not known if degrees with SMC are closed downwards.  It is also not known if every degree either has the cupping property or a SMC. In this talk we will review several of these results and present techniques used to build SMCs.


Title: Algebraic logic and algebraizable logics
=== '''February 24 -  Hongyu Zhu''' ===


Abstract: Arguably the oldest theme in what we would recognize as "mathematical logic" is the algebraic interpretation of logic, the most famous example of this being the connection between (classical) propositional logic and Boolean algebras. But underlying the subject of algebraic logic is the implicit assumption that many logical systems are "satisfyingly" interpreted as algebraic structures. This naturally hints at a question, which to my knowledge went unasked for a surprisingly long time: when does a logic admit a "nice algebraic interpretation?"
'''Title:''' tba


Perhaps surprisingly, this is actually a question which can be made precise enough to treat with interesting results. I'll sketch what is probably the first serious result along these lines, due to Blok and Pigozzi, and then say a bit about where this aspect of algebraic logic has gone from there.
'''Abstract:''' tba


=== March 16 - Spring break - No seminar ===
=== '''March 3 - Uri Andrews''' ===


'''Due to the cancellation of face-to-face instruction in UW-Madison through at least April 10, the seminar is suspended until further notice'''
'''Title:''' tba


'''Abstract:''' tba


=== '''Macrh 10 -  Logan Heath''' ===


== Fall 2019 ==
'''Title:''' tba


=== September 5 - Organizational meeting ===
'''Abstract:''' tba


=== September 9 - No seminar ===


=== September 16 - Daniel Belin ===
=== '''Macrh 17 - Yiqing Wang''' ===
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.
'''Title:''' tba


=== September 23 - Daniel Belin ===
'''Abstract:''' tba


Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
=== '''Macrh 31 - Chiara Travesset''' ===


=== September 30 - Josiah Jacobsen-Grocott ===
'''Title:''' tba


Title: Scott Rank of Computable Models
'''Abstract:''' tba


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.


=== October 7 - Josiah Jacobsen-Grocott ===


Title: Scott Rank of Computable Codels - Continued
== Fall 2024 ==


=== October 14 - Tejas Bhojraj ===
The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. We will follow notes by Noam Greenberg. If you are not enrolled but would like to audit it, please contact [mailto:soskova@wisc.edu Mariya Soskova].


Title: Solovay and Schnorr randomness for infinite sequences of qubits.
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1ect-dgHdoHOgq4-5BGFiDh6pPThLfDg69Yg__-b_5RY/edit?usp=sharing Sign up here.]


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.
Notes: [https://uwmadison.box.com/s/j3xftdj1i70d4lblxhzswhg9e25ajcpq Download the notes here.] You will need your UW-login. Please, do not distribute these notes without permission from the author.  


=== October 23 - Tejas Bhojraj ===
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


Title: Solovay and Schnorr randomness for infinite sequences of qubits - continued
=== '''September 9 - Organizational Meeting''' ===


Unusual time and place: Wednesday October 23, 4:30pm, Van Vleck B321.
Mariya Soskova will start with the first sections from the notes.


=== October 28 - Two short talks ===
We will then assign speakers to dates and topics.


'''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
=== '''September 16 -  Sections 1.2-1.4''' ===


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):
Kanav Madhura will continue with Sections 1.2-1.4.  


- Is the axiom weaker if we demand that $W$ is clopen?
=== '''September 23 - Sections 1.3-1.4 and 2.1-2.2''' ===
- 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.
Kanav Madhura will continue with Sections 1.3-1.4. Lucas Duckworth will be ready with Sections 2.1 and 2.2 should there be time.  


'''James Earnest Hanson''' - Strongly minimal sets in continuous logic
=== '''September 30 -  Sections 2.2 and 2.3-2.5''' ===


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.
Lucas Duckworth will finish Section 2.2. Karthik Ravishankar will begin 2.3, 2.4, and 2.5.
=== '''October 7th - Sections 2.4 and 2.5''' ===


=== November 4 - Two short talks ===
Karthik Ravishankar will  finish, 2.4, and 2.5.  Liang Yu will give a talk at 4:00pm.


'''Manlio Valenti''' - The complexity of closed Salem sets (20 minutes version)
=== '''October 14th -  Sections 2.6 and 2.7''' ===


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.
Bjarki Gunnarsson  will present Sections 2.6 and 2.7
<br/>
In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.  


'''Patrick Nicodemus''' - Proof theory of Second Order Arithmetic and System F
=== '''October 21th -  Section 3.1''' ===


A central theme in proof theory is to show that some formal system has the property that whenever A is provable, there is a proof of A in "normal form" - a direct proof without any detours. Such results have numerous and immediate consequences - often consistency follows as an easy corollary. The Curry Howard correspondence describes of equivalences between normalization of proofs and program termination in typed lambda calculi. We present an instance of this equivalence, between the proof theory of intuitionistic second order arithmetic and the second order polymorphic lambda calculus of Girard and Reynolds, aka system F.
Karthik Ravishankar will present Section 3.1 


=== November 11 - Manlio Valenti ===
=== '''October 28th - Sections 3.2 and 3.3''' ===


Title: The complexity of closed Salem sets (full length)
Karthik Ravishankar will finish Sections 3.2  and John Spoerl will begin Section 3.3


Abstract:
=== '''November 4th - Sections 3.3 and 3.4''' ===
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.
<br/>
In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.


=== November 18 - Iván Ongay Valverde ===
John Spoerl will finish Sections 3.3 and 3.4


Title: A couple of summer results
=== '''November 11th -  Section 4.1''' ===


Abstract: Lately, I have been studying how subsets of reals closed under Turing equivalence behave through the lenses of algebra, measure theory and orders.
Antonion Nakid-Cordero will present Section 4.1


In this talk I will classify which subsets of reals closed under Turing equivalence generate subfields or $\mathbb{Q}$-vector spaces of $\mathbb{R}$. We will show that there is a non-measurable set whose Turing closure becomes measurable (and one that stays non-measurable) and, if we have enough time, we will see a model where there are 5 possible order types for $\aleph_1$ dense subsets of reals, but just 1 for $\aleph_1$ dense subsets of reals closed under Turing equivalence.
=== '''November 19th - Sections 4.1 and 4.2''' ===


=== November 25 - Anniversary of the signing of the Treaty of Granada - No seminar ===
Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.


=== December 2 - Anniversary of the Battle of Austerlitz - No seminar ===


=== December 9 - Anniversary of the death of Pope Pius IV - No seminar ===
=== '''November 25th -  Sections 4.2 and 4.3''' ===


==Previous Years==
Back to the usual time and place. Ang Li will begin Section 4.2.
 
=== '''December 2nd -  Section 4.3''' ===
 
Ang Li will present Section 4.3.
 
=== '''December 9nd -  Section 5.1''' ===
 
Last seminar for this semester. Sapir Ben-Shahar will begin Section 5.1
 
<!-- Template
 
=== '''September 18 - xxx''' ===
'''Title:''' TBA ([https://wiki.math.wisc.edu/images/***.pdf Slides])
 
'''Abstract:''' TBA
 
-->
 
== 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 13:19, 11 February 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 B235
  • Organizer: Mariya Soskova

The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact the organizers.


Spring 2025

The seminar will be run as a 1-credit seminar Math 975. In Spring 2025, we will finish last semester's topic on Higher Computability Theory.Once we are done 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 Mariya Soskova.

Presentation Schedule: Sign up here.

Notes on Higher Computability Theory: Download the notes here. You will need your UW-login. Please, do not distribute these notes without permission from the author.


January 27 - Organizational Meeting and Sapir Ben-Shahar

Mariya Soskova will call for volunteers to sign up for presentations.

Sapir Ben-Shahar will wrap up Section 5.1

February 3 - Taeyoung Em

Taeyoung Em will present Section 5.3.

February 10 - Hongyu Zhu

Hongyu Zhu will present Section 5.3

February 17 - Karthik Ravishankar

Title: Strong minimal covers and the cupping property

Abstract: A longstanding question in degree theory has been whether every minimal Turing degree has a strong minimal cover. Meanwhile a strong example of degrees without SMC's are those which have the cupping property. It is known that PA degrees have the cupping property, as do degrees with a certain amount of escaping power. On the other hand, it is known that being weak in the sense of being non DNC and Hyperimmune-free lets you have a SMC. Degrees with the cupping property are closed upwards while it is not known if degrees with SMC are closed downwards. It is also not known if every degree either has the cupping property or a SMC. In this talk we will review several of these results and present techniques used to build SMCs.

February 24 - Hongyu Zhu

Title: tba

Abstract: tba

March 3 - Uri Andrews

Title: tba

Abstract: tba

Macrh 10 - Logan Heath

Title: tba

Abstract: tba


Macrh 17 - Yiqing Wang

Title: tba

Abstract: tba

Macrh 31 - Chiara Travesset

Title: tba

Abstract: tba


Fall 2024

The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. We will follow notes by Noam Greenberg. If you are not enrolled but would like to audit it, please contact Mariya Soskova.

Presentation Schedule: Sign up here.

Notes: Download the notes here. You will need your UW-login. Please, do not distribute these notes without permission from the author.


September 9 - Organizational Meeting

Mariya Soskova will start with the first sections from the notes.

We will then assign speakers to dates and topics.

September 16 - Sections 1.2-1.4

Kanav Madhura will continue with Sections 1.2-1.4.

September 23 - Sections 1.3-1.4 and 2.1-2.2

Kanav Madhura will continue with Sections 1.3-1.4. Lucas Duckworth will be ready with Sections 2.1 and 2.2 should there be time.

September 30 - Sections 2.2 and 2.3-2.5

Lucas Duckworth will finish Section 2.2. Karthik Ravishankar will begin 2.3, 2.4, and 2.5.

October 7th - Sections 2.4 and 2.5

Karthik Ravishankar will finish, 2.4, and 2.5. Liang Yu will give a talk at 4:00pm.

October 14th - Sections 2.6 and 2.7

Bjarki Gunnarsson will present Sections 2.6 and 2.7

October 21th - Section 3.1

Karthik Ravishankar will present Section 3.1

October 28th - Sections 3.2 and 3.3

Karthik Ravishankar will finish Sections 3.2 and John Spoerl will begin Section 3.3

November 4th - Sections 3.3 and 3.4

John Spoerl will finish Sections 3.3 and 3.4

November 11th - Section 4.1

Antonion Nakid-Cordero will present Section 4.1

November 19th - Sections 4.1 and 4.2

Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.


November 25th - Sections 4.2 and 4.3

Back to the usual time and place. Ang Li will begin Section 4.2.

December 2nd - Section 4.3

Ang Li will present Section 4.3.

December 9nd - Section 5.1

Last seminar for this semester. Sapir Ben-Shahar will begin Section 5.1


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=28089"