{
  "id": "math/0609655",
  "version": "v2",
  "published": "2006-09-25T19:55:06.000Z",
  "updated": "2007-02-17T09:59:43.000Z",
  "title": "Winning the pressing down game but not Banach Mazur",
  "authors": [
    "Jakob Kellner",
    "Matti Pauna",
    "Saharon Shelah"
  ],
  "comment": "New version: some improvements in presentation, references, history; main theorem slightly strengthened; some typos removed",
  "journal": "J. Symbolic Logic 72 (2007), No. 4, 1323--1335",
  "doi": "10.2178/jsl/1203350789",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $S$ be the set of those $\\alpha\\in\\omega_2$ that have cofinality $\\omega_1$. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length $\\omega_1$, but not the Banach Mazur game of length $\\omega+1$ (both games starting with $S$).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-17T09:59:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55"
    ],
    "keywords": [
      "banach mazur game",
      "nonempty player wins",
      "consistent",
      "cofinality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9655K"
    }
  }
}