Separation for isometric group actions and hyperimaginary independence

Abstract: In the theory of (finite) permutation groups, P. M. Neumann’s Lemma says that if a group G acts on a set X, and P is a finite subset of X such that all points of P have an infinite orbit, then for any other finite set in Q there is a group element g such that gP is disjoint from Q. When applied to the automorphism group of a first-order structure, this lemma can be used to prove a number of useful results in model theory. In this talk, I will present a metric space version of P. M. Neumman’s Lemma, along with several applications in the model theory of metric structures. For example, we show that algebraic independence in continuous logic satisfies the “full existence axiom”, answering a question of Andrews, Goldbring, and Keisler. Time permitting, I will also discuss some consequences for hyperimaginaries, which are new even in classical discrete logic. Joint work with J. Hanson.

group theorylogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic