Date/Time : 11 Nov 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Kyle Gannon, Peking University

In model theory, and in logic more broadly, we are often interested in the first-order theory of a given mathematical structure. Probabilistic constructions, however, typically produce not a single structure but a random one. For example, the first-order theory obtained by percolating edges on a graph may depend on the particular outcome of the percolation. This project addresses this issue by introducing a syntactic object, a random theory, associated with random constructions. We argue that random theories accurately encode the first-order consequences of such constructions. In this talk, we will focus on the basic definitions and examples surrounding these ideas. This is currently ongoing research with Nikolay Bazhenov and Sam Braunfeld.

Add to calendar :

Date/Time : 04 Nov 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Josiah Jacobsen-Grocott, Nanyang Technological University

Weak Turing reducibility (\le_WT) was introduced by Davis as a way of extending Turing reducibility to partial functions. This degree structure was further studied by Sasso, who coined the term “weak Turing reducibility” and compared \le_WT to the enumeration reducibility (\le_e). Sasso proved that the e-degrees are isomorphic to an initial segment of the WT-degrees among other results.

Add to calendar :

Date/Time : 28 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ye Jinhe, University of Hong Kong

The classical inverse Galois problem asks whether every finite group occurs as a Galois group over ℚ. A geometric generalization is the regular inverse Galois problem over a field K, which asks for regular realizations over K(t). For K = ℚ, such realizations yield solutions to the classical problem by Hilbert irreducibility. While the regular inverse Galois problem remains open over ℚ, it is known to have a positive solution over large fields. In this talk, I will discuss a positive solution over curve-excluding fields, which are existentially closed among fields avoiding a fixed curve and provide a class of non-large fields over which the problem can be solved.

Add to calendar :

Date/Time : 21 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nurlan Markhabatov, Eurasian National University (Astana, Kazakhstan)

This talk investigates model-theoretic properties of pseudofinite unars (where a unar is an algebra with a single unary operation). A criterion for the uncountable categoricity of pseudofinite unar theories is obtained. Examples of pseudofinite unar theories are constructed that are superstable but not ω-stable, ω-stable but not strongly minimal, and ω-stable but not uncountably categorical. It is also shown that the theory of every bounded unar is pseudofinite and ω-stable. During the talk, we will also attempt to formulate a general criterion for the pseudofiniteness of unars.

Add to calendar :

Date/Time : 14 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Jia Zekun, National University of Singapore

Post’s program asks for a structural thinness property of the complement of an r.e. set that forces Turing incompleteness. The program seemed to collapse when Yates built a complete maximal set. In the 1970s Degtev and Marchenkov revived it by relativizing Post’s notions to an r.e. equivalence relation η: nonrecursive r.e. semirecursive η-maximal sets exist, and every such set is Turing incomplete. The existence of maximal sets is strong. It is equivalent to IΣ₂ over PA⁻ + BΣ₂ (Chong–Yang), and for admissible α it holds exactly when the S₃-projectum of α is ω (Lerman). Downey conjectured that η-maximal sets are easier to obtain. In my previous talk, I showed that PA⁻ + IΣ₁ proves they exist. This talk extends that result in two directions. In each, η-maximal sets turn out to be no harder to build than Friedberg–Muchnik pairs, up to the best current results.

In reverse recursion theory, PA⁻ + IΣ₀ + BΣ₁ + EXP, the theory in which Chong and Mourad proved the Friedberg–Muchnik theorem, proves the existence of a nonrecursive r.e. semirecursive η-maximal set. Moreover, we will outline how a Post-style solution to Post’s problem can be carried out in this theory by bypassing the classical detour through η-hyperhypersimplicity.

In ordinal recursion theory, we show that every limit ordinal β admits a β-r.e. equivalence relation η and a non-β-recursive β-r.e. η-maximal set A. When the Σ₁-cofinality of β is at least its Σ₁-projectum (in particular, when β is admissible), both A and the graph of η can be made regular, tame and strongly β-r.e. This is the same hypothesis under which Friedman obtained regular, strongly β-r.e. Friedberg–Muchnik pairs under <wβ. (When the Σ₁-cofinality of β is less than its Σ₁-projectum, the Friedberg–Muchnik theorem with respect to ≤wβ is generally false and the same theorem with respect to ≤β remains open.

Add to calendar :

Date/Time : 07 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Neil Barton and Zachary Goodsell, National University of Singapore

In light of the development of forcing, philosophers and mathematicians have wondered whether the truths of mathematics might be contingent. This talk investigates that idea in the framework of higher-order logic. Our main result is that forcing-related contingency (e.g., contingency of the continuum hypothesis) is consistent in the higher-order logic Bacon and Dorr call Classicism + Rigid Comprehension, which permits quantification over both properties and modally rigid classes.

Add to calendar :

Date/Time : 23 Sep 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Péter Komjáth, Eötvös Loránd University

To be announced.

Add to calendar :

Date/Time : 16 Sep 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nikolay Bazhenov, Nanyang Technological University

In recent years, there has been renewed interest in the algorithmic aspects of various Stone-type dualities. For instance, Harrison-Trainor, Melnikov, and Ng (2020) proved that a Boolean algebra B has a computable isomorphic copy if and only if its dual Stone space St(B) is homeomorphic to a computable Polish space. In this talk, following the approach of Ershov and Schwidefsky, we work with effective presentations of topological T_0-spaces with base. We establish a computable version of a Stone-type duality due to Schwidefsky (2023), and we discuss its applications in computable topology.

This is joint work with Iskander Kalimullin and Marina Schwidefsky.

Add to calendar :

Date/Time : 02 Sep 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Erik Walsberg, University of Vienna

I will introduce trace definability between first order structures/theories and explain how it can be used to give dichotomies between linearity and field structure in certain settings.

Add to calendar :