{
  "id": "1304.7797",
  "version": "v1",
  "published": "2013-04-29T20:46:18.000Z",
  "updated": "2013-04-29T20:46:18.000Z",
  "title": "Definable closure in randomizations",
  "authors": [
    "Uri Andrews",
    "Isaac Goldbring",
    "H. Jerome Keisler"
  ],
  "comment": "19 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "The randomization of a complete first order theory T is the complete continuous theory T^R with two sorts, a sort for random elements of models of T, and a sort for events in an underlying probability space. We give necessary and sufficient conditions for an element to be definable over a set of parameters in a model of T^R.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-29T20:46:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "definable closure",
      "randomization",
      "complete first order theory",
      "random elements",
      "complete continuous theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7797A"
    }
  }
}