{
  "id": "1810.10061",
  "version": "v1",
  "published": "2018-10-23T19:26:17.000Z",
  "updated": "2018-10-23T19:26:17.000Z",
  "title": "On categoricity in successive cardinals",
  "authors": [
    "Sebastien Vasey"
  ],
  "comment": "17 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\\mathbb{L}_{\\omega_1, \\omega}$ sentence categorical on an end segment of cardinals below $\\beth_\\omega$ must be categorical also everywhere above $\\beth_\\omega$. This is done without any additional model-theoretic hypotheses (such as amalgamation or arbitrarily large models) and generalizes to the much broader framework of tame AECs with weak amalgamation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-23T19:26:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C48",
      "03C45",
      "03C52",
      "03C55",
      "03C75"
    ],
    "keywords": [
      "successive cardinals",
      "categoricity",
      "abstract elementary classes",
      "additional model-theoretic hypotheses",
      "weak amalgamation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}