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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. |
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| * '''When:''' Mondays 4p-5p | | * '''When:''' Mondays 3:30-4:30 PM |
| * '''Where:''' Van Vleck B215. | | * '''Where:''' Van Vleck B211 |
| * '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein] | | * '''Organizer:''' Joseph Miller |
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| 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. |
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| 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]--> |
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| == Spring 2020 - Tentative schedule == | | ==Fall 2025== |
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| === January 28 - Talk by visitor - No seminar ===
| | 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]. |
| === February 3 - Talk by visitor - No seminar ===
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| === February 10 - James Hanson ===
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| === February 17 - James Hanson ===
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| === February 24 - Two short talks - Tejas Bhojraj and Josiah Jacobsen-Grocott ===
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| === March 2 - Patrick Nicodemus ===
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| === March 9 - Patrick Nicodemus ===
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| === March 16 - Spring break - No seminar ===
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| === March 23 - Two short talks - Harry Main-Luu and Daniel Belin ===
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| === March 30 - Josiah Jacobsen-Grocott ===
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| === April 6 - Josiah Jacobsen-Grocott ===
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| === April 13 - Faculty at conference - No seminar ===
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| === April 20 - Harry Main-Luu ===
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| === April 27 - Harry Main-Luu ===
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| | Presentation Schedule: [https://docs.google.com/spreadsheets/d/1uRSaI1edJ5sepz57NV07ohIfBSKL9FgkvJvMAewk1ms/edit?usp=sharing Sign up here.] |
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| | <!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)--> |
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| == Fall 2019 ==
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| === September 5 - Organizational meeting === | | ==='''September 8 - Organizational Meeting'''=== |
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| === September 9 - No seminar ===
| | We will meet to arrange the schedule |
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| === September 16 - Daniel Belin === | | ==='''September 15 - Karthik Ravishankar: Contrasting the halves of an Ahmad pair''' === |
| Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic
| | 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. |
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| 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.
| | 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. |
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| === September 23 - Daniel Belin ===
| | 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. |
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| Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
| | === '''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. |
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| === September 30 - Josiah Jacobsen-Grocott === | | === '''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. |
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| Title: Scott Rank of Computable Models
| | ==='''October 6 - Dhruv Kulshreshtha''' === |
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| 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 13 - Chiara Travesset''' === |
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| === October 7 - Josiah Jacobsen-Grocott === | | ==='''October 20 -''' === |
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| Title: Scott Rank of Computable Codels - Continued
| | === '''October 27 - Yiqing Wang''' === |
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| === October 14 - Tejas Bhojraj === | | === '''November 3 - Logan Heath''' === |
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| Title: Solovay and Schnorr randomness for infinite sequences of qubits.
| | ==='''November 10 -''' === |
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| 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 17 - Hongyu Zhu''' === |
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| === October 23 - Tejas Bhojraj === | | ==='''November 24 - Taeyoung Em''' === |
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| Title: Solovay and Schnorr randomness for infinite sequences of qubits - continued
| | ==='''December 1 - Lucas Duckworth''' === |
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| Unusual time and place: Wednesday October 23, 4:30pm, Van Vleck B321.
| | ==='''December 8 -''' === |
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| === October 28 - Two short talks ===
| | == Previous Years== |
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| '''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
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| 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):
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| - Is the axiom weaker if we demand that $W$ is clopen?
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| - If the continuum is bigger than $\aleph_2$, can we ask that $H$ has the same size as $E$?
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| - Can we expand this axiom to spaces that are not second countable and metric?
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| These questions lead to different versions of SOCA. In this talk, we will analyze how they relate to the original axiom.
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| '''James Earnest Hanson''' - Strongly minimal sets in continuous logic
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| 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.
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| === November 4 - Two short talks ===
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| '''Manlio Valenti''' - The complexity of closed Salem sets (20 minutes version)
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| 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.
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| In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.
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| '''Patrick Nicodemus''' - Proof theory of Second Order Arithmetic and System F
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| 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.
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| === November 11 - Manlio Valenti ===
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| Title: The complexity of closed Salem sets (full length)
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| 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.
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| In this talk we will study the descriptive complexity of the family of closed Salem subsets of the real line.
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| === November 18 - Iván Ongay Valverde ===
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| Title: A couple of summer results
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| Abstract: Lately, I have been studying how subsets of reals closed under Turing equivalence behave through the lenses of algebra, measure theory and orders.
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| 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.
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| === November 25 - Anniversary of the signing of the Treaty of Granada - No seminar ===
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| === December 2 - Anniversary of the Battle of Austerlitz - No seminar ===
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| === December 9 - Anniversary of the death of Pope Pius IV - No seminar ===
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| ==Previous Years== | |
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| 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]]. |
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
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.