{
  "id": "1201.0382",
  "version": "v2",
  "published": "2012-01-01T20:24:08.000Z",
  "updated": "2012-11-26T20:18:51.000Z",
  "title": "The $ \\mathbfΣ^1_2$ counterparts to statements that are equivalent to the Continuum Hypothesis",
  "authors": [
    "Asger Tornquist",
    "William Weiss"
  ],
  "comment": "Several minor corrections throughout. Finally submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "We consider natural $\\Sigma^1_2$ definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these $\\Sigma^1_2$ analogues are equivalent to that all reals are constructible. We also prove two partition relations for $\\Sigma^1_2$ colourings which hold precisely when there is a non-constructible real.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-26T20:18:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E45",
      "03E50"
    ],
    "keywords": [
      "continuum hypothesis",
      "equivalent",
      "counterparts",
      "partition relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.0382T"
    }
  }
}