{
  "id": "1406.3306",
  "version": "v2",
  "published": "2014-06-12T18:04:23.000Z",
  "updated": "2015-06-05T17:08:11.000Z",
  "title": "Quotients of Strongly Proper Forcings and Guessing Models",
  "authors": [
    "Sean Cox",
    "John Krueger"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have simple universal strongly generic conditions on a stationary set of models by certain nice regular suborders satisfy the $\\omega_1$-approximation property. We prove that the existence of stationarily many $\\omega_1$-guessing models in $P_{\\omega_2}(H(\\theta))$, for sufficiently large cardinals $\\theta$, is consistent with the continuum being arbitrarily large, solving a problem of Viale and Weiss.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-12T18:04:23.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-05T17:08:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E40",
      "03E35"
    ],
    "keywords": [
      "guessing models",
      "simple universal strongly generic conditions",
      "nice regular suborders satisfy",
      "approximation property",
      "strongly proper forcing posets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3306C"
    }
  }
}