Work

Automorphism groups of prime models, and invariant measures

Year: 2025

Type: article

Abstract: We adapt the notion from [7] and [2] of a (relatively) definable subset of A u t ( M ) when M is a saturated structure, to the case A u t ( M / A ) when M is atomic and strongly ω -homogeneous (over a set A ). We discuss the existence and uniqueness of invariant measures on the Boolean algebra of definable subsets of A u t ( M / A ) . For example when T is stable, we have existence and uniqueness. We also discuss the compatibility of our definability notions with definable Galois cohomology from [12] and differential Galois theory.

Source: Annals of Pure and Applied Logic

DOI: 10.1016/j.apal.2025.103568

Author: Anand Pillay

Institution: University of Notre Dame

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funder: National Science Foundation