{
  "id": "math/0504196",
  "version": "v3",
  "published": "2005-04-10T16:58:30.000Z",
  "updated": "2008-07-08T01:33:42.000Z",
  "title": "Model theory without choice: Categoricity",
  "authors": [
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in aleph_alpha for some (equivalently for every) ordinal alpha>0. Another central result here is, in this context: the number of models of a countable first order T of cardinality aleph_alpha is either >=|alpha| for every aleph_\\alpha or it has a small upper bound (close to beth_2).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-07-08T01:33:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "model theory",
      "categoricity",
      "small upper bound",
      "morley theorem",
      "los conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4196S"
    }
  }
}