{
  "id": "1707.09008",
  "version": "v1",
  "published": "2017-07-27T19:23:04.000Z",
  "updated": "2017-07-27T19:23:04.000Z",
  "title": "Tameness from two successive good frames",
  "authors": [
    "Sebastien Vasey"
  ],
  "comment": "23 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show, assuming a mild set-theoretic hypothesis, that if an abstract elementary class (AEC) has a superstable-like forking notion for models of cardinality $\\lambda$ and a superstable-like forking notion for models of cardinality $\\lambda^+$, then orbital types over saturated models of cardinality $\\lambda^+$ are determined by their restrictions to submodels of cardinality $\\lambda$. By a superstable-like forking notion, we mean here a good frame, a central concept of Shelah's book on AECs. It is known that locality of orbital types together with the existence of a superstable-like notion for models of cardinality $\\lambda$ implies the existence of a superstable-like notion for models of cardinality $\\lambda^+$, but here we prove the converse. An immediate consequence is that forking in $\\lambda^+$ can be described in terms of forking in $\\lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-27T19:23:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C48",
      "03C45",
      "03C52",
      "03C55",
      "03C75"
    ],
    "keywords": [
      "superstable-like forking notion",
      "cardinality",
      "orbital types",
      "mild set-theoretic hypothesis",
      "abstract elementary class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}