{
  "id": "2405.11878",
  "version": "v1",
  "published": "2024-05-20T08:42:56.000Z",
  "updated": "2024-05-20T08:42:56.000Z",
  "title": "Automorphism groups of prime models, and invariant measures",
  "authors": [
    "Anand Pillay"
  ],
  "comment": "16 pages",
  "categories": [
    "math.LO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-20T08:42:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "12H05",
      "12G05"
    ],
    "keywords": [
      "invariant measures",
      "automorphism groups",
      "prime models",
      "differential galois theory",
      "definable subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}