{
  "id": "1404.2111",
  "version": "v3",
  "published": "2014-04-08T12:59:10.000Z",
  "updated": "2015-06-03T12:41:27.000Z",
  "title": "Absoluteness via Resurrection",
  "authors": [
    "Giorgio Audrito",
    "Matteo Viale"
  ],
  "comment": "25 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "The resurrection axioms are forms of forcing axioms that were introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Velickovic. We introduce a stronger form of resurrection axioms (the iterated resurrection axioms) and show that they imply generic absoluteness for the first-order theory of $H_{\\mathfrak{c}}$ with parameters with respect to various classes of forcing. We also show that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. We also compare these results with the generic absoluteness results by Woodin and the second author.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-01T10:29:36.000Z",
      "comment": "15 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-06-03T12:41:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E57"
    ],
    "keywords": [
      "generic absoluteness results",
      "stationary set preserving posets",
      "second author",
      "supercompact cardinals",
      "stronger form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2111A"
    }
  }
}