{
  "id": "1505.06296",
  "version": "v1",
  "published": "2015-05-23T09:59:46.000Z",
  "updated": "2015-05-23T09:59:46.000Z",
  "title": "Two inequalities between cardinal invariants",
  "authors": [
    "Dilip Raghavan",
    "Saharon Shelah"
  ],
  "comment": "11 pages, submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove two $\\mathrm{ZFC}$ inequalities between cardinal invariants. The first inequality involves cardinal invariants associated with an analytic P-ideal, in particular the ideal of subsets of $\\omega$ of asymptotic density $0$. We obtain an upper bound on the $\\ast$-covering number, sometimes also called the weak covering number, of this ideal by proving in Section \\ref{sec:covz0} that ${\\mathord{\\mathrm{cov}}}^{\\ast}({\\mathcal{Z}}_{0}) \\leq \\mathfrak{d}$. In Section \\ref{sec:skbk} we investigate the relationship between the bounding and splitting numbers at regular uncountable cardinals. We prove in sharp contrast to the case when $\\kappa = \\omega$, that if $\\kappa$ is any regular uncountable cardinal, then ${\\mathfrak{s}}_{\\kappa} \\leq {\\mathfrak{b}}_{\\kappa}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-23T09:59:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "03E55",
      "03E05",
      "03E20"
    ],
    "keywords": [
      "regular uncountable cardinal",
      "analytic p-ideal",
      "upper bound",
      "sharp contrast",
      "asymptotic density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506296R"
    }
  }
}