{
  "id": "1408.2839",
  "version": "v2",
  "published": "2014-08-12T20:23:46.000Z",
  "updated": "2015-08-17T18:43:04.000Z",
  "title": "On the Splitting Number at Regular Cardinals",
  "authors": [
    "Omer Ben-Neria",
    "Moti Gitik"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $\\kappa$,$\\lambda$ be regular uncountable cardinals such that $\\lambda > \\kappa^+$ is not a successor of a singular cardinal of low cofinality. We construct a generic extension with $s(\\kappa) = \\lambda$ starting from a ground model in which $o(\\kappa) = \\lambda$ and prove that assuming $\\neg 0^{\\P}$, $s(\\kappa) = \\lambda$ implies that $o(\\kappa) \\geq \\lambda$ in the core model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-12T20:23:46.000Z",
      "abstract": "Let $\\kappa$,$\\lambda$ be regular uncountable cardinals such that $\\kappa^+ < \\lambda$. We construct a generic extension with $s(\\kappa) = \\lambda$ starting from a ground model in which $o(\\kappa) = \\lambda$ and prove that assuming $\\neg 0^{\\P}$, $s(\\kappa) = \\lambda$ implies that $o(\\kappa) \\geq \\lambda$ in the core model.",
      "comment": "17 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-17T18:43:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E10",
      "03E17",
      "03E35",
      "03E55"
    ],
    "keywords": [
      "regular cardinals",
      "splitting number",
      "regular uncountable cardinals",
      "ground model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2839B"
    }
  }
}