Automorphism groups of prime models, and invariant measures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917670836764672 |
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| author | Pillay, Anand |
| author_facet | Pillay, Anand |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of prime models, and invariant measures Pillay, Anand Logic 03C45, 12H05, 12G05 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. |
| title | Automorphism groups of prime models, and invariant measures |
| topic | Logic 03C45, 12H05, 12G05 |
| url | https://arxiv.org/abs/2405.11878 |