Automorphism groups of prime models, and invariant measures

Anand Pillay

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arXiv · 2405.11878

Automorphism groups of prime models, and invariant measures

Anand Pillay

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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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BibTeX RIS

Anand Pillay. 2024-05-20. Automorphism groups of prime models, and invariant measures. https://arxiv.org/abs/2405.11878

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