{
  "id": "math/0501527",
  "version": "v1",
  "published": "2005-01-28T22:49:51.000Z",
  "updated": "2005-01-28T22:49:51.000Z",
  "title": "The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis",
  "authors": [
    "Justin Tatch Moore"
  ],
  "comment": "7 pages",
  "journal": "Ann. Pure Appl. Logic 140 (2006), no. 1-3, 128--132",
  "doi": "10.1016/j.apal.2005.09.011",
  "categories": [
    "math.LO"
  ],
  "abstract": "The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA. While the results fall short of showing that MRP implies SCH, it will be shown that MRP implies that if SCH fails first at kappa then every stationary subset of S_{kappa^+}^omega = {a < kappa^+ : cf(a) = omega} reflects. It will also be demonstrated that MRP always fails in a generic extension by Prikry forcing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-28T22:49:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E10",
      "03E75"
    ],
    "keywords": [
      "singular cardinals hypothesis",
      "proper forcing axiom",
      "prikry forcing",
      "set mapping reflection principle",
      "results fall short"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1527T"
    }
  }
}