{
  "id": "1110.5037",
  "version": "v2",
  "published": "2011-10-23T12:12:19.000Z",
  "updated": "2012-08-03T18:47:17.000Z",
  "title": "Forcing Axioms and the Continuum Hypothesis, part II: Transcending ω_1-sequences of real numbers",
  "authors": [
    "Justin Tatch Moore"
  ],
  "comment": "12 pages. fixed a few typographical errors",
  "categories": [
    "math.LO"
  ],
  "abstract": "The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah. The corresponding completely proper forcing which can be constructed using CH is moreover a tree whose square is special off the diagonal. While such trees had previously been constructed by Jensen and Kunen under the assumption of Jensen's diamond principle, this is the first time such a construction has been carried out using the Continuum Hypothesis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-03T18:47:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E50",
      "03E57"
    ],
    "keywords": [
      "continuum hypothesis",
      "forcing axiom",
      "real numbers",
      "jensens diamond principle",
      "first time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5037T"
    }
  }
}