{
  "id": "1006.1808",
  "version": "v1",
  "published": "2010-06-09T14:19:06.000Z",
  "updated": "2010-06-09T14:19:06.000Z",
  "title": "Pcf theory and cardinal invariants of the reals",
  "authors": [
    "Lajos Soukup"
  ],
  "comment": "9 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "The additivity spectrum ADD(I) of an ideal I is the set of all regular cardinals kappa such that there is an increasing chain {A_alpha:alpha<kappa\\} in the ideal I such that the union of the chain is not in I. We investigate which set A of regular cardinals can be the additivity spectrum of certain ideals. Assume that I=B or I=N, where B denotes the sigma-ideal generated by the compact subsets of the Baire space omega^omega, and N is the ideal of the null sets. For countable sets we give a full characterization of the additivity spectrum of I: a non-empty countable set A of uncountable regular cardinals can be ADD(I) in some c.c.c generic extension iff A=pcf(A).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-09T14:19:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E04",
      "03E17",
      "03E35"
    ],
    "keywords": [
      "cardinal invariants",
      "pcf theory",
      "additivity spectrum add",
      "regular cardinals kappa",
      "null sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1808S"
    }
  }
}