{
  "id": "1403.5757",
  "version": "v1",
  "published": "2014-03-23T14:41:16.000Z",
  "updated": "2014-03-23T14:41:16.000Z",
  "title": "A generalization of Solovay's $Σ$-construction with application to intermediate models",
  "authors": [
    "Vladimir Kanovei"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1402.0961",
  "categories": [
    "math.LO"
  ],
  "abstract": "A $\\Sigma$-construction of Solovay is extended to the case of intermediate sets which are not necessarily subsets of the ground model, with a more transparent description of the resulting forcing notion than in the classical paper of Grigorieff. As an application, we prove that, for a given name $t$ (not necessarily a name of a subset of the ground model), the set of all sets of the form $t[G]$ (the $G$-interpretation of $t$), $G$ being generic over the ground model, is Borel. This result was first established by Zapletal by a descriptive set theoretic argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-23T14:41:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E40",
      "03E15"
    ],
    "keywords": [
      "intermediate models",
      "ground model",
      "application",
      "construction",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5757K"
    }
  }
}