Ronnie Chen : Étale structures in countable model theory and descriptive set theory

Posted by Matthew Harrison-Trainor , part of the Logic Seminar.

At

March 4, 2025, 3:30 p.m.

In

636 SEO

Abstract

A standard technique in countable model theory is to define a topological space "continuously parametrizing" countable structures in some language, and then apply methods of descriptive set theory and topological dynamics to model-theoretic questions.  In fact several versions of such a "space of models" are known, all of which are instances of the notion of an étale bundle (aka sheaf) of structures.  We will give an introduction to the theory of étale bundles, and survey some of the countable model-theoretic machinery that may be naturally generalized to this context, including the Lopez-Escobar theorem, characterizations of Scott rank, and groupoid representations.