{
  "id": "math/9511205",
  "version": "v3",
  "published": "1995-11-30T00:00:00.000Z",
  "updated": "1998-07-09T00:36:01.000Z",
  "title": "Transferring saturation, the finite cover property, and stability",
  "authors": [
    "J. Baldwin",
    "R. Grossberg",
    "Saharon Shelah"
  ],
  "comment": "This version replaces the 1995 submission: Characterization of the finite cover property and stability. This version submitted by John T. Baldwin. The paper has been accepted for the Journal of Symbolic Logic",
  "categories": [
    "math.LO"
  ],
  "abstract": "Saturation is (mu,kappa)-transferable in T if and only if there is an expansion T_1 of T with |T_1| = |T| such that if M is a mu-saturated model of T_1 and |M| \\geq kappa then the reduct M|L(T) is kappa-saturated. We characterize theories which are superstable without the finite cover property (f.c.p.), or without f.c.p. as, respectively those where saturation is (aleph_0,lambda)-transferable or (kappa(T),lambda)-transferable for all lambda. Further if for some mu \\geq |T|, 2^mu > mu^+, stability is equivalent to: or all mu \\geq |T|, saturation is (\\mu,2^mu)-transferable.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1998-07-09T00:36:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite cover property",
      "transferring saturation",
      "mu-saturated model",
      "characterize theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math.....11205B"
    }
  }
}