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arXiv:2405.11878 [math.LO]AbstractReferencesReviewsResources

Automorphism groups of prime models, and invariant measures

Anand Pillay

Published 2024-05-20Version 1

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.

Comments: 16 pages
Categories: math.LO
Subjects: 03C45, 12H05, 12G05
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