{
  "id": "math/0509707",
  "version": "v1",
  "published": "2005-09-29T21:38:53.000Z",
  "updated": "2005-09-29T21:38:53.000Z",
  "title": "Abstract decomposition theorem and applications",
  "authors": [
    "Rami Grossberg",
    "Olivier Lessmann"
  ],
  "comment": "36 pages",
  "journal": "Contemporary Mathematics, Vol 380, (2005), pp. 73--108",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-29T21:38:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C52",
      "03C05",
      "03C95"
    ],
    "keywords": [
      "abstract decomposition theorem",
      "applications",
      "first order tehory",
      "abstract elementary class",
      "main gap result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9707G"
    }
  }
}