John E. Solak : Why it's so Hard to Talk to Your Topologist Friends

Posted by John Solak , part of the Louise Hay Logic Seminar.

At

Feb. 17, 2025, 3 p.m.

In

612 SEO

Abstract

It is common Model Theory lore that topological spaces are not first order i.e. cannot be fully captured in first order Logic. More formally, we say that topologies do not form an elementary class in any (reasonable) language. Yet, determining how to prove this seems to be a challenging task. In this talk, I will showcase various mode-theoretic results about "suitable" languages as evidence of this claim. I will assume familiarity with introductory Model Theory. Knowledge of the Compactness and Lowenheim-Skolem Theorems is recommended.