{
  "id": "math/0509387",
  "version": "v2",
  "published": "2005-09-16T19:18:11.000Z",
  "updated": "2005-09-19T11:47:36.000Z",
  "title": "Shelah's Categoricity Conjecture from a successor for Tame Abstract Elementary Classes",
  "authors": [
    "Rami Grossberg",
    "Monica VanDieren"
  ],
  "comment": "19 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let K be an Abstract Elemenetary Class satisfying the amalgamation and the joint embedding property, let \\mu be the Hanf number of K. Suppose K is tame. MAIN COROLLARY: (ZFC) If K is categorical in a successor cardinal bigger than \\beth_{(2^\\mu)^+} then K is categorical in all cardinals greater than \\beth_{(2^\\mu)^+}. This is an improvment of a Theorem of Makkai and Shelah ([Sh285] who used a strongly compact cardinal for the same conclusion) and Shelah's downward categoricity theorem for AECs with amalgamation (from [Sh394]).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-19T11:47:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C35",
      "03C45",
      "03C75"
    ],
    "keywords": [
      "tame abstract elementary classes",
      "shelahs categoricity conjecture",
      "abstract elemenetary class",
      "successor cardinal bigger",
      "shelahs downward categoricity theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9387G"
    }
  }
}