Exchangeability and invariant Keisler measures in omega-categorical structures

Authors: Samuel Walker Braunfeld
Publication year: 2025
Publication type: Abstrakt
Periodical: Schedule for Infinite Structural Ramsey Theory
Bibliographic citation: BRAUNFELD, Samuel Walker. Exchangeability and invariant Keisler measures in omega-categorical structures. In: Schedule for Infinite Structural Ramsey Theory. Banff: BIRSC, 2025. Dostupné z: https://www.birs.ca/events/2025/5-day-workshops/25w5398/schedule
ID: 649345
Online record: View online record

Abstract

BASIC DATA: Invited talk presented at BIRS workshop on Infinite Structural Ramsey Theory. 23.11.2025-28.11.2025, Banff. ABSTRACT: Given an omega-categorical structure M, we consider the problem of classifying Aut(M)-invariant Keisler measures, i.e. finitely-additive probability measures on definable sets. By passing to a more general question about invariant random expansions and making use of exchangeability from probability theory, we resolve this problem in many cases. Our techniques, namely the random placement construction and a sort of multi-amalgamation, are very reminiscent of techniques in structural Ramsey theory. This is joint work with Colin Jahel and Paolo Marimon.