{
  "id": "math/9212202",
  "version": "v1",
  "published": "1992-12-02T00:00:00.000Z",
  "updated": "1992-12-02T00:00:00.000Z",
  "title": "A large Pi-1-2 set absolute for set forcing",
  "authors": [
    "Sy D. Friedman"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let k be a definable L-cardinal. Then there is a set of reals X, class-generic over L, such that L(X) and L have the same cardinals, X has size k in L(X) and some pi-1-2 formula defines X in all set-generic extensions of L(X). Two corollaries, both assuming the consistency of an inaccessible: It is consistent for the Perfect Set Property to hold for boldface sigma-1-2 sets, yet fail for some lightface pi-1-2 set. It is consistent that the Perfect Set Property holds for boldface sigma-1-2 sets yet some lightface pi-1-2 wellordering of some set of reals has length aleph-1000.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-12-02T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set absolute",
      "set forcing",
      "perfect set property holds",
      "formula defines",
      "set-generic extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math.....12202F"
    }
  }
}