{
  "id": "1005.5534",
  "version": "v2",
  "published": "2010-05-30T14:21:18.000Z",
  "updated": "2010-06-05T07:10:49.000Z",
  "title": "Linear ROD subsets of Borel partial orders are countably cofinal in Solovay's model",
  "authors": [
    "Vladimir Kanovei"
  ],
  "comment": "5 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "The following is true in the Solovay model. 1. If $\\leq$ is a Borel partial quasi-order on a Borel set $D$ of the reals, $X$ is a ROD subset of $D$, and $\\leq$ restricted to $X$ is linear, then $X$ is countably cofinal in the sense of $\\leq$. 2. If in addition every countable set $Y$ of $D$ has a strict upper bound in the sense of $\\leq$, then the ordering $< D ; \\leq >$ has no maximal chains that are ROD sets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-05T07:10:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15"
    ],
    "keywords": [
      "linear rod subsets",
      "borel partial orders",
      "countably cofinal",
      "solovays model",
      "borel partial quasi-order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5534K"
    }
  }
}