{
  "id": "1110.1181",
  "version": "v2",
  "published": "2011-10-06T08:36:00.000Z",
  "updated": "2012-02-09T12:48:03.000Z",
  "title": "Martin's maximum revisited",
  "authors": [
    "Matteo Viale"
  ],
  "comment": "31 pages, updated versions will be available on the author's webpage: http://www2.dm.unito.it/paginepersonali/viale/",
  "categories": [
    "math.LO"
  ],
  "abstract": "We present several results relating the general theory of the stationary tower forcing developed by Woodin with forcing axioms. The main results is that the forcing axiom MM^{++} (also known as MM^{+\\omega_1}) decides the \\Pi_2-theory of H_{\\omega_2} with respect to stationary set preserving forcings. We argue that this is a close to optimal generalization to H_{\\omega_2} of Woodin's absoluteness results for L(R).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-09T12:48:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martins maximum",
      "woodins absoluteness results",
      "stationary set preserving forcings",
      "forcing axiom",
      "optimal generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1181V"
    }
  }
}