{
  "id": "math/0307229",
  "version": "v2",
  "published": "2003-07-16T19:56:05.000Z",
  "updated": "2004-02-24T19:34:24.000Z",
  "title": "Extensions with the approximation and cover properties have no new large cardinals",
  "authors": [
    "Joel David Hamkins"
  ],
  "comment": "25 pages. While preserving the main ideas, the new version makes a number of changes in presentation, such as a new title and reorganized order of results, and corrects an issue concerning definable classes and amenability",
  "categories": [
    "math.LO"
  ],
  "abstract": "If an extension Vbar of V satisfies the delta approximation and cover properties for classes and V is a class in Vbar, then every suitably closed embedding j:Vbar to Nbar in Vbar with critical point above delta restricts to an embedding j|V:V to N amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above delta. This result extends work in math.LO/9808011.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-02-24T19:34:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E55",
      "03E40"
    ],
    "keywords": [
      "large cardinals",
      "cover properties",
      "result extends work",
      "delta approximation",
      "extension vbar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7229H"
    }
  }
}