{
  "id": "1205.4275",
  "version": "v2",
  "published": "2012-05-18T22:22:05.000Z",
  "updated": "2015-12-07T14:51:15.000Z",
  "title": "Square principles in Pmax extensions",
  "authors": [
    "Andrés Eduardo Caicedo",
    "Paul Larson",
    "Grigor Sargsyan",
    "Ralf Schindler",
    "John Steel",
    "Martin Zeman"
  ],
  "comment": "Revised version, incorporating the referee's suggestions",
  "categories": [
    "math.LO"
  ],
  "abstract": "By forcing with $\\mathbb{P}_{\\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\\omega_2$ and $\\omega_3$ fail. In particular, we obtain a model of $2^{\\aleph_0}=2^{\\aleph_1}=\\aleph_2 + \\lnot\\square(\\omega_2) + \\lnot\\square(\\omega_3)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-18T22:22:05.000Z",
      "abstract": "By forcing with Pmax over strong models of determinacy, we obtain models where different square principles at omega_2 and omega_3 fail. In particular, we obtain a model of 2^{aleph_0}=2^{aleph_1}=aleph_2 + square(omega_2) fails + square(omega_3) fails.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Andres Caicedo",
        "Paul Larson",
        "Grigor Sargsyan",
        "Ralf Schindler",
        "John Steel",
        "Martin Zeman"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-12-07T14:51:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E60",
      "03E57",
      "03E55",
      "03E45",
      "03E35"
    ],
    "keywords": [
      "square principles",
      "pmax extensions",
      "strong models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.4275C"
    }
  }
}