{
  "id": "math/9911228",
  "version": "v1",
  "published": "1999-11-28T22:40:16.000Z",
  "updated": "1999-11-28T22:40:16.000Z",
  "title": "On versions of clubsuit on cardinals larger than aleph_1",
  "authors": [
    "Mirna Džamonja",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We give two results on guessing unbounded subsets of lambda^+. The first is a positive result and applies to the situation of lambda regular and at least equal to aleph_3, while the second is a negative consistency result which applies to the situation of lambda a singular strong limit with 2^lambda>lambda^+. The first result shows that in ZFC there is a guessing of unbounded subsets of S^{lambda^+}_lambda. The second result is a consistency result (assuming a supercompact cardinal exists) showing that a natural guessing fails. A result of Shelah in math.LO/9808140 shows that if 2^lambda=lambda^+ and lambda is a strong limit singular, then the corresponding guessing holds. Both results are also connected to an earlier result of Dzamonja and Shelah in which they showed that a certain version of clubsuit holds at a successor of singular just in ZFC. The first result here shows that a result of math.LO/9601219 can to a certain extent be extended to the successor of a regular. The negative result here gives limitations to the extent to which one can hope to extend this result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-11-28T22:40:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E35",
      "04A20"
    ],
    "keywords": [
      "cardinals larger",
      "first result",
      "unbounded subsets",
      "singular strong limit",
      "strong limit singular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11228D"
    }
  }
}