{
  "id": "math/0212312",
  "version": "v6",
  "published": "2002-12-22T21:22:47.000Z",
  "updated": "2010-10-31T19:02:48.000Z",
  "title": "The combinatorics of splittability",
  "authors": [
    "Boaz Tsaban"
  ],
  "comment": "Small updates",
  "journal": "Annals of Pure and Applied Logic 129 (2004), 107--130",
  "doi": "10.1016/j.apal.2003.03.001",
  "categories": [
    "math.LO",
    "math.CA",
    "math.CO",
    "math.GN"
  ],
  "abstract": "Marion Scheepers, in his studies of the combinatorics of open covers, introduced the property Split(U,V) asserting that a cover of type U can be split into two covers of type V. In the first part of this paper we give an almost complete classification of all properties of this form where U and V are significant families of covers which appear in the literature (namely, large covers, omega-covers, tau-covers, and gamma-covers), using combinatorial characterizations of these properties in terms related to ultrafilters on N. In the second part of the paper we consider the questions whether, given U and V, the property Split(U,V) is preserved under taking finite unions, arbitrary subsets, powers or products. Several interesting problems remain open.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2010-10-31T19:02:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "54D20",
      "54D80"
    ],
    "keywords": [
      "combinatorics",
      "property split",
      "splittability",
      "interesting problems remain open",
      "marion scheepers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12312T"
    }
  }
}