Automorphism groups of prime models, and invariant measures

Anand Pillay

Automorphism groups of prime models, and invariant measures

Logic 2024-05-21 v1

Authors: Anand Pillay

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.

Keywords

Automorphism groups prime models invariant measures definable subsets saturated models stable theories

Cite

@article{arxiv.2405.11878,
  title  = {Automorphism groups of prime models, and invariant measures},
  author = {Anand Pillay},
  journal= {arXiv preprint arXiv:2405.11878},
  year   = {2024}
}

Comments

16 pages

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