{
  "id": "0911.5124",
  "version": "v3",
  "published": "2009-11-26T17:17:48.000Z",
  "updated": "2011-09-06T02:48:21.000Z",
  "title": "A simultaneous generalization of independence and disjointness in boolean algebras",
  "authors": [
    "Corey Thomas Bruns"
  ],
  "comment": "Sumbitted to Order",
  "doi": "10.1007/s11083-011-9237-x",
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-06T02:48:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03G05",
      "03E17"
    ],
    "keywords": [
      "simultaneous generalization",
      "independence",
      "boolean algebras generalizing free boolean",
      "algebras generalizing free boolean algebras",
      "disjointness"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5124B"
    }
  }
}