{
  "id": "2110.15411",
  "version": "v6",
  "published": "2021-10-28T19:48:07.000Z",
  "updated": "2022-07-14T07:31:23.000Z",
  "title": "Remarks on convergence of Morley sequences",
  "authors": [
    "Karim Khanaki"
  ],
  "comment": "(23 pages) In this new version (1) a model-theoretic argument of Claim 2 in Theorem 2.11 is suggested by Predrag Tanovi\\'c, (2) Claim 0 in Theorem 2.11 has been proven, (3) Fact 2.10 has been rewritten. (Theorem 4.10 reinforces the main result of the following paper on the model-theoretic meaning of Grothendieck's double limit theorem: arXiv:1703.04761 )",
  "categories": [
    "math.LO"
  ],
  "abstract": "We refine results of Gannon [G21, Theorem 4.7] and Simon [S15a, Lemma 2.8] on equivalences of convergent Morley sequences. We then introduce the notion of eventual $NIP$, as a property of a model, and give a variant of [KP18, Corollary 2.2]. Finally, we give new characterizations of generically stable types (for countable theories) and reinforce the main result of Pillay [P18] on the model-theoretic meaning of Grothendieck's double limit theorem.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2022-07-14T07:31:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45"
    ],
    "keywords": [
      "convergence",
      "grothendiecks double limit theorem",
      "convergent morley sequences",
      "main result",
      "refine results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}