{
  "id": "1608.05691",
  "version": "v1",
  "published": "2016-08-19T18:37:12.000Z",
  "updated": "2016-08-19T18:37:12.000Z",
  "title": "On a class of maximality principles",
  "authors": [
    "Daisuke Ikegami",
    "Nam Trang"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study various classes of maximality principles, $\\rm{MP}(\\kappa,\\Gamma)$, introduced by J.D. Hamkins, where $\\Gamma$ defines a class of forcing posets and $\\kappa$ is a cardinal. We explore the consistency strength and the relationship of $\\textsf{MP}(\\kappa,\\Gamma)$ with various forcing axioms when $\\kappa \\in\\{\\omega,\\omega_1\\}$. In particular, we give a characterization of bounded forcing axioms for a class of forcings $\\Gamma$ in terms of maximality principles MP$(\\omega_1,\\Gamma)$ for $\\Sigma_1$ formulas. A significant part of the paper is devoted to studying the principle MP$(\\kappa,\\Gamma)$ where $\\kappa\\in\\{\\omega,\\omega_1\\}$ and $\\Gamma$ defines the class of stationary set preserving forcings. We show that MP$(\\kappa,\\Gamma)$ has high consistency strength; on the other hand, if $\\Gamma$ defines the class of proper forcings or semi-proper forcings, then by Hamkins, it is shown that MP$(\\kappa,\\Gamma)$ is consistent relative to $V=L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-19T18:37:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "forcing axioms",
      "maximality principles mp",
      "stationary set preserving forcings",
      "high consistency strength",
      "significant part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}