2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Logic in Canada IV
Org: Bradd Hart (McMaster University) and Rahim Moosa (University of Waterloo)
[PDF]
Org: Bradd Hart (McMaster University) and Rahim Moosa (University of Waterloo)
[PDF]
- DIEGO BAJERANO, York
- CHRISTINE EAGLES, University of Waterloo
Algebraic independence of solutions to multiple Lotka-Volterra systems [PDF]
- CHRISTINE EAGLES, University of Waterloo
-
A major problem in recent applications of the model theory of DCF$_0$ is determining when a given system of algebraic differential equations defines a strongly minimal set. A definable set $S$ is strongly minimal if it is infinite and for any other definable set $R$ (over any set of
parameters), either $S\cap R$ or $S\setminus R$ is finite. In joint work with Yutong Duan and Léo Jimenez, we classify exactly when the solution set to a Lotka-Volterra system is strongly minimal. In the strongly minimal case, we classify all algebraic relations between Lotka-Volterra systems and show that for any distinct solutions $x_1,...,x_n$ (not in the algebraic closure of the base field $F$), $\mathrm{trdeg}(x_1, \cdots, x_m/F) = 2m$.
- ALI HAMAD, University of Ottawa
Bundles of metric structures as left ultrafunctors [PDF]
-
The ultraproduct construction play a fundamental role in both classic and continuous first-order logic. Categorical treatment of that construction can be done in the framework of ultracategories first introduced by Makkai and then by Lurie, where it was used in classic model theoretic and topos theoretic settings. We have used this new framework to study categories of models of continuous logic, and showed a result related to bundle theory. A certain class of functors from a compact Hausdorff space to the category of models of a continuous theory is equivalent to a nice enough notion of bundles of models of this theory, with the compact Hausdorff space being the base space. This notion allows for the recovery of familiar notions of bundles like Banach bundles and continuous fields of $\mathrm{C}^*$ algebras.
- LEO JIMENEZ, Ohio State
- JOEY LAKERDAS-GAYLE, Waterloo
- ILGWON SEO, McMaster
- MATHIAS STOUT, McMaster
- CAROLINE TERRY, UIC
- SPENCER UNGER, UofT
- JOEY LAKERDAS-GAYLE, Waterloo