{
  "id": "math/0605022",
  "version": "v1",
  "published": "2006-04-30T14:07:30.000Z",
  "updated": "2006-04-30T14:07:30.000Z",
  "title": "A connection between decomposable ultrafilters and possible cofinalities. II",
  "authors": [
    "Paolo Lipparini"
  ],
  "comment": "6 pages",
  "journal": "Published as \"Decomposable ultrafilters and possible cofinalities\" on Notre Dame Journal of Formal Logic 49, 307--312 (2008).",
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "We use Shelah's theory of possible cofinalities in order to solve a problem about ultrafilters. THEOREM. Suppose that $ \\lambda $ is a singular cardinal, $ \\lambda ' < \\lambda $, and the ultrafilter $D$ is $ \\kappa $-decomposable for all regular cardinals $ \\kappa $ with $ \\lambda ' < \\kappa < \\lambda $. Then $D$ is either $ \\lambda $-decomposable, or $ \\lambda ^+$-decomposable. We give applications to topological spaces and to abstract logics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-30T14:07:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C20",
      "03E04",
      "03C95",
      "54D20"
    ],
    "keywords": [
      "decomposable ultrafilters",
      "cofinalities",
      "connection",
      "shelahs theory",
      "singular cardinal"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5022L"
    }
  }
}