{
  "id": "1608.05726",
  "version": "v1",
  "published": "2016-08-19T20:12:50.000Z",
  "updated": "2016-08-19T20:12:50.000Z",
  "title": "PFA and guessing models",
  "authors": [
    "Nam Trang"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "This paper explores the consistency strength of The Proper Forcing Axiom ($\\textsf{PFA}$) and the theory (T) which involves a variation of the Viale-Wei$\\ss$ guessing hull principle. We show that (T) is consistent relative to a supercompact cardinal. The main result of the paper implies that the theory \"$\\sf{AD}$$_\\mathbb{R} + \\Theta$ is regular\" is consistent relative to (T) and to $\\textsf{PFA}$. This improves significantly the previous known best lower-bound for consistency strength for (T) and $\\textsf{PFA}$, which is roughly \"$\\sf{AD}$$_\\mathbb{R} + \\textsf{DC}$\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-19T20:12:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E45",
      "03E55",
      "03E47"
    ],
    "keywords": [
      "guessing models",
      "consistency strength",
      "paper implies",
      "main result",
      "proper forcing axiom"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}