{
  "id": "1004.0741",
  "version": "v5",
  "published": "2010-04-06T00:14:03.000Z",
  "updated": "2013-07-14T17:57:28.000Z",
  "title": "Model theory of operator algebras II: Model theory",
  "authors": [
    "Ilijas Farah",
    "Bradd Hart",
    "David Sherman"
  ],
  "comment": "20 pages; references are not missing this time",
  "categories": [
    "math.LO",
    "math.OA"
  ],
  "abstract": "We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on N are isomorphic even when the Continuum Hypothesis fails.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-07-14T17:57:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "46L10",
      "03C20",
      "03C98"
    ],
    "keywords": [
      "model theory",
      "operator algebras",
      "tracial von neumann algebras",
      "continuum hypothesis fails",
      "purely model-theoretic result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.0741F"
    }
  }
}