{
  "id": "math/0510004",
  "version": "v1",
  "published": "2005-09-30T21:00:00.000Z",
  "updated": "2005-09-30T21:00:00.000Z",
  "title": "Categoricity from one successor cardinal in Tame Abstract Elementary Classes",
  "authors": [
    "Rami Grossberg",
    "Monica VanDieren"
  ],
  "comment": "20 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is \\chi-tame. If K is categorical in some \\lambda^+ >LS(K) then it is categorical in all \\mu\\geq (\\lambda+\\chi)^+. Theorem 2. If K is LS(K)-tame and is categorical both in LS(K) and in LS(K)^+ then K is categorical in all \\mu\\geq LS(K).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-30T21:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C52",
      "03C75"
    ],
    "keywords": [
      "tame abstract elementary classes",
      "successor cardinal",
      "categoricity",
      "joint embedding properties",
      "arbitrarily large models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10004G"
    }
  }
}