{
  "id": "0804.0775",
  "version": "v1",
  "published": "2008-04-04T15:51:23.000Z",
  "updated": "2008-04-04T15:51:23.000Z",
  "title": "Some consequences of reflection on the approachability ideal",
  "authors": [
    "Assaf Sharon",
    "Matteo Viale"
  ],
  "comment": "11 pages, updated versions available at the author's webpage",
  "categories": [
    "math.LO",
    "math.AC"
  ],
  "abstract": "We study the approachability ideal I[\\kappa^+] in the context of large cardinals properties of the regular cardinals below a singular \\kappa. As a guiding example consider the approachability ideal I[\\aleph_{\\omega+1}] assuming that \\aleph_\\omega is strong limit. In this case we obtain that club many points in \\aleph_{\\omega+1} of cofinality \\aleph_n for some n>1 are approachable assuming the joint reflection of countable families of stationary subsets of \\aleph_n. This reflection principle holds under Martin's maximum for all n>1 and for each n>1 is equiconsistent with \\aleph_n being weakly compact in L. This characterizes the structure of the approachability ideal I[\\aleph_{\\omega+1}] in models of Martin's maximum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-04T15:51:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E04",
      "03E55"
    ],
    "keywords": [
      "approachability ideal",
      "consequences",
      "martins maximum",
      "large cardinals properties",
      "reflection principle holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0775S"
    }
  }
}