Automorphism groups of prime models, and invariant measures

2024/05/20 by Anand Pillay, Pillay, Anand
Mathematics · #03C45 #12G05 #12H05 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2405.11878

openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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