{
  "id": "0805.1548",
  "version": "v1",
  "published": "2008-05-11T21:13:40.000Z",
  "updated": "2008-05-11T21:13:40.000Z",
  "title": "Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. IV",
  "authors": [
    "Paolo Lipparini"
  ],
  "comment": "10 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We extend to singular cardinals the model-theoretical relation $\\lambda \\stackrel{\\kappa}{\\Rightarrow} \\mu$ introduced in P. Lipparini, The compactness spectrum of abstract logics, large cardinals and combinatorial principles, Boll. Unione Matematica Italiana ser. VII, {\\bf 4-B} 875--903 (1990). We extend some results obtained in Part II, finding equivalent conditions involving uniformity of ultrafilters and the existence of certain infinite matrices. Our present definition suggests a new compactness property for abstract logics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-11T21:13:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C20",
      "03E05",
      "03C95",
      "03C55",
      "03C98"
    ],
    "keywords": [
      "model-theoretical principles",
      "topological spaces",
      "ultrafilters",
      "combinatorial",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1548L"
    }
  }
}