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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 an space focus principally in  practicing presentation skills or learning materials that are not usually presented on 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, 4:00 PM – 5:00 PM (unless otherwise announced).
* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' Van Vleck B235 (unless otherwise announced).
* '''Where:''' Van Vleck B223
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]
* '''Organizers:''' [https://uriandrews.netlify.app/ Uri Andrews] and [https://sites.google.com/view/hongyu-zhu/ Hongyu Zhu]


Talks schedule are arrange and decide 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.


== Spring 2018 ==
Sign up for the graduate logic seminar mailing list:  [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu]


=== January 29, Organizational meeting ===
== Fall 2023 ==


This day we decided the schedule for the semester.
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].


=== February 5, [http://www.math.wisc.edu/~andrews/ Uri Andrews] ===
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.


Title: Building Models of Strongly Minimal Theories - Part 1
Presentation Schedule: https://docs.google.com/spreadsheets/d/15Qd4EzrrKpn1Ct5tur1P_FDc2czsdAVnUf_pfp65Lb4/edit?usp=sharing


Abstract: Since I'm talking in the Tuesday seminar as well, I'll use the Monday seminar talk to do some background on the topic and some
Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)
lemmas that will go into the proofs in Tuesday's talk. There will be (I hope) some theorems of interest to see on both days, and both on
the general topic of answering the following question: What do you need to know about a strongly minimal theory in order to compute
copies of all of its countable models. I'll start with a definition for strongly minimal theories and build up from there.


=== February 12, James Hanson ===
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.


Title: Finding Definable Sets in Continuous Logic
=== September 11 - Organizational Meeting ===


Abstract: In order to be useful the notion of a 'definable set' in continuous logic is stricter than a naive comparison to discrete logic
We will meet to assign speakers to dates.
would suggest. As a consequence, even in relatively tame theories there can be very few definable sets. For example, there is a
superstable theory with no non-trivial definable sets. As we'll see, however, there are many definable sets in omega-stable,
omega-categorical, and other small theories.


=== February 19, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
=== '''September 18 - Taeyoung Em''' ===
'''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])


Title: Proper forcing
'''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.


Abstract: Although a given forcing notion may have nice properties on its own, those properties might vanish when we apply it repeatedly.
=== '''September 25 - Karthik Ravishankar''' ===
Early preservation results (that is, theorems saying that the iteration of forcings with a nice property retains that nice property)
'''Title:''' Spectra of structures
were fairly limited, and things really got off the ground with Shelah's invention of "proper forcing." Roughly speaking, a forcing is
proper if it can be approximated by elementary submodels of the universe in a particularly nice way. I'll define proper forcing and
sketch some applications.


=== February 26, Patrick Nicodemus ===
'''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.


Title: A survey of computable and constructive mathematics in economic history
=== '''October 2 - Hongyu Zhu''' ===
'''Title:''' Continuum Hypothesis: On Platonism and Pluralism ([https://wiki.math.wisc.edu/images/CH.pdf Slides] and [https://uwmadison.zoom.us/rec/share/lSe2BL28988PGmmthWKA6FM7bWOJ0eR6vxP4laS7O6ImNN2gQ5skPJ6-C8KlbGcm.G48mQQ0qlW-lo3gr Recording]; Passcode: .iXJs?1t)


=== March 5, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===
'''Abstract:''' Despite its independence from ZFC, the continuum hypothesis continues to be of interest to logicians. In this talk, we will see arguments for settling the truth of CH in one way or another (or yet another). We will see how mathematical arguments (the inner model program) are intertwined with philosophical beliefs (mathematical Platonism and pluralism) about the set-theoretic universe(s).


Title: Convexly Orderable Groups
=== '''October 9 - Hannah Ashbach ''' ===
'''Title:''' An Introduction to Constructive Mathematics ([https://wiki.math.wisc.edu/images/An_Introduction_to_Constructive_Mathematics.pdf Slides] and [https://uwmadison.zoom.us/rec/share/UIxI2m2WWMnitZTd1oQxYxl6vpashJdvf_2UtN6erlFXN9yNgm7q0mhXw1min0-L.cz3b7tsbBPlsgxD6 Recording]; Passcode: 5.$c5L+2)


=== March 12, [https://math.nd.edu/people/visiting-faculty/daniel-turetsky/ Dan Turetsky] (University of Notre Dame) ===
'''Abstract:''' Have you ever written a mathematical proof and felt dissatisfied after writing QED? Perhaps you had proven the existence of a particularly complicated mathematical object, but you have no clue how that object may actually look or be constructed. Or perhaps you are ready to denounce the Axiom of Choice after reading about its far-reaching consequences. Constructive logic is a formal logic system that seeks to clear up these concerns for mathematicians, though not all mathematicians agree with the power it holds-- or takes away.


Title: Structural Jump
=== '''October 16 - Rune Chen ''' ===
'''Title:''' An Introduction to Model-Theoretic Galois Theory


=== March 19, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===
'''Abstract:''' Given an arbitrary first-order theory with elimination of imaginaries, the standard Galois theory can be translated into a model-theoretic version, which can be further generalized and thus be useful in other algebraic settings. In this talk, we will give a brief introduction to model-theoretic Galois theory and then look at a simple case of model-theoretic Galois correspondence. We will skip the detailed discussion of elimination of imaginaries by choosing our theory T to be a first-order theory coding finite sets and working in a large enough saturated model M of T.


Title: Networks and degrees of points in non-second countable spaces
=== '''October 23 - John Spoerl ''' ===
'''Title:''' The Computational Content of Forcing


=== April 2, Wil Cocke ===
'''Abstract:''' Given information about a ground model, how much can you know about it’s forcing extensions? Given a forcing extension, how much can you know about its ground model? This talk will be a primer on forcing and a review of the main results of Hamkins, Miller and Williams’ 2020 paper: “Forcing as a Computational Process”.


Title: Characterizing Finite Nilpotent Groups via Word Maps
=== '''October 30 - Chiara Travesset ''' ===
'''Title:''' Mission-time LTL (MLTL) Formula Validation Via Regular Expressions


Abstract: In this talk, we will examine a novel characterization of finite nilpotent groups using the probability distributions induced by word maps. In particular we show that a finite group is nilpotent if and only if every surjective word map has fibers of uniform size.
'''Abstract:''' Mission-time Linear Temporal Logic (mLTL) is an extension of propositional logic that includes temporal operators over finite intervals of time. A computation is a (finite) sequence consisting of a truth assignment for each propositional variable at each time step. This presentation will describe how we can use regular expressions to describe the structure of the computations that make a given mLTL formula true. We prove soundness and completeness, and also give an implemented algorithm (the WEST program) and analyze its complexity both theoretically and experimentally. We generate a test suite using control flow diagrams to robustly test the code. Finally, we present the REST theorem, which significantly simplifies certain sets of computations. This talk only requires basic familiarity with propositional logic and computer science.


=== April 9, Tejas Bhojraj ===
=== '''November 6 - Antonio Nakid Cordero ''' ===
'''Title:''' Martin's Conjecture in the Turing degrees and the Enumeration Degrees


Title: Quantum Randomness
'''Abstract:''' Martin's Conjecture is an attempt to formalize the empirical phenomenon that "naturally occurring" Turing degrees are well-ordered. In this talk, I'll go over how one can make that into a precise mathematical statement, a uniform version of the conjecture that has been fully resolved, and some of the complications of trying to propose a similar conjecture in the enumeration degrees. If time allows, I'll report on my ongoing project in this direction.


Abstract: I will read the paper by Nies and Scholz where they define a notion of algorithmic randomness for infinite sequences of quantum bits (qubits). This talk will cover the basic notions of quantum randomness on which my talk on Tuesday will be based.  
=== '''November 13 - Alice Vidrine ''' ===
'''Title:''' Enumeration Weihrauch degrees and closed choice problems ([https://wiki.math.wisc.edu/images/EWdeg_Grad_seminar_Fall_23.pdf Slides] and [https://uwmadison.zoom.us/rec/share/F_pDYkWhHGiMTy7Rkqrb_PpeJnjxBCo0ZIMOEHV4CP-XfJodbV-P8igStgVwiXq4.A7ONs9u5Em6-3Gvp Recording] Passcode: C89k#5&0)


=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===
'''Abstract:''' In the Weihrauch degrees, we think of elements of Baire space as names for elements of mathematical objects. In the enumeration Weihrauch (eW) degrees we follow a similar idea, but our names may only carry positive information. It turns out that this coding by positive information separates several choice problems that are equivalent in the Weihrauch degrees, and in this talk we look at some of the more striking examples and their proofs. We close with some discussion of various directions for further research.


Title: What can we say about sets made by the union of Turing equivalence classes?
=== '''November 20 - Logan Heath ''' ===
'''Title:''' A Proof Theorist's Guide to First Aid: CUT-Elimination and Other Results of Classical Proof Theory ([https://wiki.math.wisc.edu/images/A_Proof_Theorist%27s_Guide_to_First_Aid.pdf Slides])


Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?
'''Abstract:''' When are correct proofs also "bad" proofs, how can we avoid them, and should we even try? In this talk we examine some early results of classical proof theory regarding the consistency of the sequent calculus for FOL and '''PA'''. In both cases our approach will be to avoid proofs which are technically correct, but also defective in some sense.


This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.
=== November 27 - Thanksgiving Break ===
=== '''December 4 - Mei Rose Connor ''' ===
'''Title:''' When ‘And’ is Too Much and ‘Or’ is Not Enough


This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation.(hopefully).
'''Abstract:''' This work was motivated by the seven–valued predication system of the Jaina religion, which states that no statement exists as an absolute. This system, known as ''Saptabhangivada'' in Sanskrit, has 7 truth values that are the non-empty subsets of the set {asti, nāsti, avaktavyah}. These words translate to: ''it is'', ''it is not'', and ''it is unassertible'', respectively. This talk will explore how these seven truth values relate to each other, the problems encountered when trying to formalise this system, and the author’s current resolution of said problems using lattice theory and introducing an eighth truth value.


=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) Start 3:45 Room B231===
=== '''December 11 - Ang Li ''' ===
'''Title:''' TBA


Title: Cototal enumeration degrees and their applications to effective mathematics
'''Abstract:''' TBA


Abstract: The enumeration degrees measure the relative computational difficulty of enumerating sets of natural numbers. Unlike the Turing degrees, the enumeration degrees of a set and its complement need not be comparable. A set is total if it is enumeration above its complement. Taken together, the enumeration degrees of total sets form an embedded copy of the Turing degrees within the enumeration degrees. A set of natural numbers is cototal if it is enumeration reducible to its complement. Surprisingly, the degrees of cototal sets, the cototal degrees, form an intermediate structure strictly between the total degrees and the enumeration degrees.
<!-- Template


Jeandel observed that cototal sets appear in a wide class of structures: as the word problems of simple groups, as the languages of minimal subshifts, and more generally as the maximal points of any c.e. quasivariety. In the case of minimal subshifts, the enumeration degree of the subshift's language determines the subshift's Turing degree spectrum: the collection of Turing degrees obtained by the points of the subshift. We prove that cototality precisely characterizes the Turing degree spectra of minimal subshifts: the degree spectra of nontrivial minimal subshifts are precisely the cototal enumeration cones. On the way to this result, we will give several other characterizations of the cototal degrees, including as the degrees of maximal anti-chain complements on <math>\omega^{<\omega}</math>, and as the degrees of enumeration-pointed trees on <math>2^{<\omega}</math>, and we will remark on some additional applications of these characterizations.
=== '''September 18 - Karthik Ravishankar''' ===
'''Title:''' Lowness for Isomorphism ([https://wiki.math.wisc.edu/images/Karthik_talk.pdf Slides])


=== April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===
'''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.


Title: Definibility of the Frobenius orbits and an application to sets of rational distances.
-->


Abstract: In this talk I'll present a paper by Hector Pastén. We will talk about how having a formula that identify a Frobenius orbits can help you show an analogue case of Hilbert's tenth problem (the one asking for an algorithm that tells you if a diophantine equation is solvable or not).
== Previous Years ==


Finally, if time permits, we will do an application that solves the existence of a dense set in the plane with rational distances, assuming some form of the ABC conjecture. This last question was propose by Erdös and Ulam.
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].
 
== Fall 2017 ==
 
=== September 11, Organizational meeting ===
 
This day we decided the schedule for the semester.
 
=== September 18, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
 
Title: The Kunen inconsistency
 
Abstract: While early large cardinal axioms were usually defined combinatorially - e.g., cardinals satisfying a version of Ramsey's
theorem - later focus shifted to model-theoretic definitions, specifically definitions in terms of elementary embeddings of the
whole universe of sets. At the lowest level, a measurable cardinal is one which is the least cardinal moved (= critical point) by a
nontrivial elementary embedding from V into some inner model M.
 
There are several variations on this theme yielding stronger and stronger large cardinal notions; one of the most important is the
inclusion of *correctness properties* of the target model M. The strongest such correctness property is total correctness: M=V. The
critical point of an elementary embedding from V to V is called a *Reinhardt cardinal*. Shortly after their introduction in Reinhardt's
thesis, however, the existence of a Reinhardt cardinal was shown to be inconsistent with ZFC.
 
I'll present this argument, and talk a bit about the role of choice.
 
=== September 25, [https://sites.google.com/a/wisc.edu/schweber/ Noah Schweber] ===
 
Title: Hindman's theorem via ultrafilters
 
Abstract: Hindman's theorem is a Ramsey-type theorem in additive combinatorics: if we color the natural numbers with two colors, there is an infinite set such that any *finite sum* from that set has the same color as any other finite sum. There are (to my knowledge) two proofs of Hindman's theorem: one of them is a complicated mess of combinatorics, and the other consists of cheating wildly. We'll do.
 
=== October 2, James Hanson ===
 
Title: The Gromov-Hausdorff metric on type space in continuous logic
 
Abstract: The Gromov-Hausdorff metric is a notion of the 'distance' between two metric spaces. Although it is typically studied in the context of compact or locally compact metric spaces, the definition is sensible even when applied to non-compact metric spaces, but in that context it is only a pseudo-metric: there are non-isomorphic metric spaces with Gromov-Hausdorff distance 0. This gives rise to an equivalence relation that is slightly coarser than isomorphism. There are continuous first-order theories which are categorical with regards to this equivalence relation while failing to be isometrically categorical, so it is natural to look for analogs of the Ryll-Nardzewski theorem and Morley's theorem, but before we can do any of that, it'll be necessary to learn about the "topometric" structure induced on type space by the Gromov-Hausdorff metric.
 
=== October 9, James Hanson ===
 
Title: Morley rank and stability in continuous logic
 
Abstract: There are various ways of counting the 'size' of subsets of metric spaces. Using these we can do a kind of Cantor-Bendixson analysis on type spaces in continuous first-order theories, and thereby define a notion of Morley rank. More directly we can define
> the 'correct' notion of stability in the continuous setting. There are also natural Gromov-Hausdorff (GH) analogs of these notions. With this we'll prove that inseparably categorical theories have atomic models over arbitrary sets, which is an important step in the proof of Morley's theorem in this setting. The same proof with essentially cosmetic changes gives that inseparably GH-categorical theories have 'GH-atomic' models over arbitrary sets, but GH-atomic models fail to be GH-unique in general.
 
=== October 23, [http://www.math.wisc.edu/~makuluni/ Tamvana Makulumi] ===
 
Title: Boxy sets in ordered convexly-orderable structures.
 
=== October 30, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===
 
Title: Dancing SCCA and other Coloring Axioms
 
Abstract: In this talk I will talk about some axioms that are closely related to SOCA (Semi Open Coloring Axiom), being the main protagonist SCCA (Semi Clopen Coloring Axiom). I will give a motivation on the statements of both axioms, a little historic perspective and showing that both axioms coincide for separable Baire spaces. This is a work in progress, so I will share some open questions that I'm happy to discuss.
 
=== November 6, Wil Cocke ===
 
Title: Two new characterizations of nilpotent groups
 
Abstract: We will give two new characterizations of finite nilpotent groups. One using information about the order of products of elements of prime order and the other using the induced probability distribution from word maps.
 
Or...
 
Title: Centralizing Propagating Properties of Groups
 
Abstract: We will examine some sentences known to have finite spectrum when conjoined with the theory of groups. Hopefully we will be able to find new examples.
 
=== November 13, [https://www.math.wisc.edu/~lempp/ Steffen Lempp] ===
 
Title: The computational complexity of properties of finitely presented groups
 
Abstract: I will survey index set complexity results on finitely presented groups.
 
=== November 20, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] ===
 
Title: Strong Difference Randomness
 
Abstract: The difference randoms were introduced by Franklin and Ng to characterize the incomplete Martin-Löf randoms. More recently, Bienvenu and Porter introduced the strong difference randoms, obtained by imposing the Solovay condition over the class of difference tests. I will give a Demuth test characterization of the strong difference randoms, along with a lowness characterization of them among the Martin-Löf randoms.
 
=== December 4, Tejas Bhojraj ===
 
Title: Quantum Algorithmic Randomness
 
Abstract: I will discuss the recent paper by Nies and Scholz where they define quantum Martin-Lof randomness (q-MLR) for infinite sequences of qubits. If time permits, I will introduce the notion of quantum Solovay randomness and show that it is equivalent to q-MLR in some special cases.
 
=== December 11, Grigory Terlov ===
 
Title: The Logic of Erdős–Rényi Graphs
 
==Previous Years==
 
The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].

Revision as of 03:18, 27 November 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.

October 2 - Hongyu Zhu

Title: Continuum Hypothesis: On Platonism and Pluralism (Slides and Recording; Passcode: .iXJs?1t)

Abstract: Despite its independence from ZFC, the continuum hypothesis continues to be of interest to logicians. In this talk, we will see arguments for settling the truth of CH in one way or another (or yet another). We will see how mathematical arguments (the inner model program) are intertwined with philosophical beliefs (mathematical Platonism and pluralism) about the set-theoretic universe(s).

October 9 - Hannah Ashbach

Title: An Introduction to Constructive Mathematics (Slides and Recording; Passcode: 5.$c5L+2)

Abstract: Have you ever written a mathematical proof and felt dissatisfied after writing QED? Perhaps you had proven the existence of a particularly complicated mathematical object, but you have no clue how that object may actually look or be constructed. Or perhaps you are ready to denounce the Axiom of Choice after reading about its far-reaching consequences. Constructive logic is a formal logic system that seeks to clear up these concerns for mathematicians, though not all mathematicians agree with the power it holds-- or takes away.

October 16 - Rune Chen

Title: An Introduction to Model-Theoretic Galois Theory

Abstract: Given an arbitrary first-order theory with elimination of imaginaries, the standard Galois theory can be translated into a model-theoretic version, which can be further generalized and thus be useful in other algebraic settings. In this talk, we will give a brief introduction to model-theoretic Galois theory and then look at a simple case of model-theoretic Galois correspondence. We will skip the detailed discussion of elimination of imaginaries by choosing our theory T to be a first-order theory coding finite sets and working in a large enough saturated model M of T.

October 23 - John Spoerl

Title: The Computational Content of Forcing

Abstract: Given information about a ground model, how much can you know about it’s forcing extensions? Given a forcing extension, how much can you know about its ground model? This talk will be a primer on forcing and a review of the main results of Hamkins, Miller and Williams’ 2020 paper: “Forcing as a Computational Process”.

October 30 - Chiara Travesset

Title: Mission-time LTL (MLTL) Formula Validation Via Regular Expressions

Abstract: Mission-time Linear Temporal Logic (mLTL) is an extension of propositional logic that includes temporal operators over finite intervals of time. A computation is a (finite) sequence consisting of a truth assignment for each propositional variable at each time step. This presentation will describe how we can use regular expressions to describe the structure of the computations that make a given mLTL formula true. We prove soundness and completeness, and also give an implemented algorithm (the WEST program) and analyze its complexity both theoretically and experimentally. We generate a test suite using control flow diagrams to robustly test the code. Finally, we present the REST theorem, which significantly simplifies certain sets of computations. This talk only requires basic familiarity with propositional logic and computer science.

November 6 - Antonio Nakid Cordero

Title: Martin's Conjecture in the Turing degrees and the Enumeration Degrees

Abstract: Martin's Conjecture is an attempt to formalize the empirical phenomenon that "naturally occurring" Turing degrees are well-ordered. In this talk, I'll go over how one can make that into a precise mathematical statement, a uniform version of the conjecture that has been fully resolved, and some of the complications of trying to propose a similar conjecture in the enumeration degrees. If time allows, I'll report on my ongoing project in this direction.

November 13 - Alice Vidrine

Title: Enumeration Weihrauch degrees and closed choice problems (Slides and Recording Passcode: C89k#5&0)

Abstract: In the Weihrauch degrees, we think of elements of Baire space as names for elements of mathematical objects. In the enumeration Weihrauch (eW) degrees we follow a similar idea, but our names may only carry positive information. It turns out that this coding by positive information separates several choice problems that are equivalent in the Weihrauch degrees, and in this talk we look at some of the more striking examples and their proofs. We close with some discussion of various directions for further research.

November 20 - Logan Heath

Title: A Proof Theorist's Guide to First Aid: CUT-Elimination and Other Results of Classical Proof Theory (Slides)

Abstract: When are correct proofs also "bad" proofs, how can we avoid them, and should we even try? In this talk we examine some early results of classical proof theory regarding the consistency of the sequent calculus for FOL and PA. In both cases our approach will be to avoid proofs which are technically correct, but also defective in some sense.

November 27 - Thanksgiving Break

December 4 - Mei Rose Connor

Title: When ‘And’ is Too Much and ‘Or’ is Not Enough

Abstract: This work was motivated by the seven–valued predication system of the Jaina religion, which states that no statement exists as an absolute. This system, known as Saptabhangivada in Sanskrit, has 7 truth values that are the non-empty subsets of the set {asti, nāsti, avaktavyah}. These words translate to: it is, it is not, and it is unassertible, respectively. This talk will explore how these seven truth values relate to each other, the problems encountered when trying to formalise this system, and the author’s current resolution of said problems using lattice theory and introducing an eighth truth value.

December 11 - Ang Li

Title: TBA

Abstract: TBA


Previous Years

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

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