{
  "id": "1503.08781",
  "version": "v2",
  "published": "2015-03-30T18:34:55.000Z",
  "updated": "2015-04-13T16:21:27.000Z",
  "title": "Chains of saturated models in AECs",
  "authors": [
    "Will Boney",
    "Sebastien Vasey"
  ],
  "comment": "40 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. Under a natural superstability assumption (which follows from categoricity in a high-enough cardinal), we prove: $\\mathbf{Theorem}$ If $K$ is a tame superstable AEC with amalgamation, then for all high-enough $\\lambda$: * The union of an increasing chain of $\\lambda$-saturated models is $\\lambda$-saturated. * There exists a type-full good $\\lambda$-frame with underlying class the saturated models of size $\\lambda$. * There exists a unique limit model of size $\\lambda$. Our proofs use independence calculus and a generalization of averages to this non first-order context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-30T18:34:55.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-13T16:21:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C48",
      "03C45",
      "03C52",
      "03C55"
    ],
    "keywords": [
      "saturated models",
      "tame abstract elementary classes",
      "non first-order context",
      "natural superstability assumption",
      "unique limit model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150308781B"
    }
  }
}