Submission date: 20 May 2024

Abstract:

We adapt the notion of a (relatively) definable subset of Aut(M) when M is a saturated model to the case Aut(M/A) when M is atomic and strongly omega-homogeneous over A. We discuss the existence and uniqueness of invariant measures on the Boolean algebra of definable subsets of Aut(M/A). For example when Th(M) is stable we have existence and uniqueness. We also discuss the compatibility of our definability notions with definable Galois cohomology and differential Galois theory.

Mathematics Subject Classification: 03C45, 12H05, 12G05

Keywords and phrases:

Full text arXiv 2405.11878: pdf, ps.