{
  "id": "1412.0195",
  "version": "v1",
  "published": "2014-11-30T08:33:25.000Z",
  "updated": "2014-11-30T08:33:25.000Z",
  "title": "On countable cofinality and decomposition of definable thin orderings",
  "authors": [
    "Vladimir Kanovei",
    "Vassily Lyubetsky"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1408.1202",
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that in some cases definable thin sets (including chains) of Borel partial orderings are necessarily countably cofinal. This includes the following cases: analytic thin sets, ROD thin sets in the Solovay model, and $\\Sigma^1_2$ thin sets in the assumption that $\\omega_1^{L[x]}<\\omega_1$ for all reals $x$. We also prove that definable thin wellorderings admit partitions into definable chains in the Solovay model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-30T08:33:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E04",
      "03E40"
    ],
    "keywords": [
      "definable thin orderings",
      "countable cofinality",
      "decomposition",
      "solovay model",
      "definable thin wellorderings admit partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0195K"
    }
  }
}