{
  "id": "math/9201249",
  "version": "v1",
  "published": "1992-01-15T00:00:00.000Z",
  "updated": "1992-01-15T00:00:00.000Z",
  "title": "Coding and reshaping when there are no sharps",
  "authors": [
    "Saharon Shelah",
    "Lee Stanley"
  ],
  "journal": "Math. Sci. Res. Inst. Publ. 26 (1992), 407--416",
  "categories": [
    "math.LO"
  ],
  "abstract": "Assuming 0^sharp does not exist, kappa is an uncountable cardinal and for all cardinals lambda with kappa <= lambda < kappa^{+ omega}, 2^lambda = lambda^+, we present a ``mini-coding'' between kappa and kappa^{+ omega}. This allows us to prove that any subset of kappa^{+ omega} can be coded into a subset, W of kappa^+ which, further, ``reshapes'' the interval [kappa, kappa^+), i.e., for all kappa < delta < kappa^+, kappa = (card delta)^{L[W cap delta]}. We sketch two applications of this result, assuming 0^sharp does not exist. First, we point out that this shows that any set can be coded by a real, via a set forcing. The second application involves a notion of abstract condensation, due to Woodin. Our methods can be used to show that for any cardinal mu, condensation for mu holds in a generic extension by a set forcing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-01-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cap delta",
      "cardinals lambda",
      "set forcing",
      "second application",
      "abstract condensation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......1249S"
    }
  }
}