Graduate Logic Seminar

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 B139
• Organizers: Karthik Ravishankar and Antonio Nakid Cordero

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 2022

September 12 - Organizational Meeting

We will meet to assign speakers to dates.

September 19 - Karthik Ravishankar

Title: Lowness for Isomorphism

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.

September 26 - Antonio Nakid Cordero

Title: When Models became Polish: an introduction to the Topological Vaught Conjecture (Slides)

Abstract: Vaught's Conjecture, originally asked by Vaught in 1961, is one of the most (in)famous open problems in mathematical logic. The conjecture is that a complete theory on a countable language must either have countably-many or continuum-many non-isomorphic models. In this talk, we will discuss some of the main ideas that surround this conjecture, with special emphasis on a topological generalization in terms of the continuous actions of Polish groups.

October 10 - Yunting Zhang

Title: Some History of Logic (Slides)

Abstract: The lives of great thinkers are sometimes overshadowed by their achievements-and there is perhaps no better illustration of this phenomenon than the life and work of Gödel. Take a look at Gödel's own timeline and see how wars and other mathematicians influenced him.

October 17 - Alice Vidrine

Title: Local operators, bilayer Turing reducibility, and enumeration Weihrauch degrees (Slides)

Abstract: Realizability toposes have a rich variety of subtoposes, corresponding to their local operators. These local operators are somewhat difficult to study in their usual form, which seems far removed from the usual objects of computability theoretic study. Recent work by Takayuki Kihara has given a characterization of the local operators on the effective topos in computability theoretic terms related to Weihrauch reduction, and which generalizes to several other realizability toposes of possible interest to computability theorists. This narrative-focused talk outlines what a realizability topos looks like, what local operators are, what Kihara's bilayer Turing reduction looks like, and how this leads to preliminary questions about a relative of the Weihrauch degrees based on enumeration reduction.

October 24 - Hongyu Zhu

Title: Investigating Natural Theories through the Consistency Operator (Slides)

Abstract: The phenomenon that "natural" theories tend to be linearly ordered in terms of consistency strength is a long-standing mystery. One approach to solving the problem is Martin's Conjecture, which roughly claims that the only natural functions on the Turing degrees are transfinite iterates of the Turing jump. In this talk we will focus on a similar approach, working inside the Lindenbaum algebra of elementary arithmetic instead of the Turing degrees. Here, the consistency operator takes the role of the jump. We will see that while some nice analogous claims can be established, there are also counterexamples that prevent us from strengthening the results in various ways.

Previous Years

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