{
  "id": "math/9707225",
  "version": "v1",
  "published": "1997-07-15T00:00:00.000Z",
  "updated": "1997-07-15T00:00:00.000Z",
  "title": "Not collapsing cardinals <= kappa in (< kappa) --support iterations",
  "authors": [
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We deal with the problem of preserving various versions of completeness in (< kappa) --support iterations of forcing notions, generalizing the case ``S --complete proper is preserved by CS iterations for a stationary co-stationary S subseteq omega_1''. We give applications to Uniformization and the Whitehead problem. In particular, for a strongly inaccessible cardinal kappa and a stationary set S subseteq kappa with fat complement we can have uniformization for < A_delta : delta in S'>, A_delta subseteq delta = sup A_delta, cf(delta)=otp(A_delta) and a stationary non-reflecting set S' subseteq S .",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-07-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "support iterations",
      "collapsing cardinals",
      "subseteq delta",
      "stationary non-reflecting set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......7225S"
    }
  }
}