{
  "id": "0811.2610",
  "version": "v2",
  "published": "2008-11-17T20:52:20.000Z",
  "updated": "2008-11-18T02:16:11.000Z",
  "title": "Variations of Independence in Boolean Algebras",
  "authors": [
    "Corey Thomas Bruns"
  ],
  "comment": "PhD thesis",
  "categories": [
    "math.LO"
  ],
  "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. Ideal-independence is also considered, and it is shown that the cardinal function p <= s_mm for infinite boolean algebras. We also define and consider moderately generated boolean algebras; that is, those boolean algebras that have a generating set consisting of elements that split finitely many elements of the boolean algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-18T02:16:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03G05",
      "03E17"
    ],
    "keywords": [
      "variations",
      "algebras generalizing free boolean algebras",
      "boolean algebras generalizing free boolean",
      "cardinal function",
      "independence"
    ],
    "tags": [
      "dissertation"
    ],
    "publication": {
      "journal": "Ph.D. Thesis",
      "year": 2008,
      "month": "Nov"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhDT.......311B"
    }
  }
}