{
  "id": "1411.2987",
  "version": "v1",
  "published": "2014-11-11T21:18:25.000Z",
  "updated": "2014-11-11T21:18:25.000Z",
  "title": "Omitting types in logic of metric structures",
  "authors": [
    "Ilijas Farah",
    "Menachem Magidor"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The present paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenestein, Henson and Usvyatsov. While a complete type is omissible in a model of a complete theory if and only if it is not principal, this is not true for incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a model of a theory $\\bfT$ in a separable language. More precisely, we find a theory in a separable language such that the set of types omissible in some of its models is a complete $\\bSigma^1_2$ set and a complete theory in a separable language such that the set of types omissible in some of its models is a complete $\\bPi^1_1$ set. We also construct a complete theory and countably many types that are separately omissible, but not jointly omissible, in its models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-11T21:18:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric structures",
      "omitting types",
      "complete theory",
      "separable language",
      "ben yaacov"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2987F"
    }
  }
}