{
  "id": "1207.1548",
  "version": "v2",
  "published": "2012-07-06T08:00:38.000Z",
  "updated": "2012-08-10T08:51:12.000Z",
  "title": "A saturation property of structures obtained by forcing with a compact family of random variables",
  "authors": [
    "Jan Krajicek"
  ],
  "comment": "preprint February 2012",
  "journal": "Archive for Mathematical Logic, 52(1), pp.19-28, (2013)",
  "doi": "10.1007/s00153-012-0304-9",
  "categories": [
    "math.LO"
  ],
  "abstract": "A method how to construct Boolean-valued models of some fragments of arithmetic was developed in Krajicek (2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family (called compactness in K.(2011)) the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-10T08:51:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C90",
      "03C50",
      "03H99"
    ],
    "keywords": [
      "random variables",
      "saturation property",
      "compact family",
      "pseudo-finite sample space",
      "existential types"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.1548K"
    }
  }
}