{
  "id": "1506.03433",
  "version": "v1",
  "published": "2015-06-10T19:39:15.000Z",
  "updated": "2015-06-10T19:39:15.000Z",
  "title": "Automorphisms of $\\mathscr{P}(λ)/\\mathscr{I}_κ$",
  "authors": [
    "Paul Larson",
    "Paul McKenney"
  ],
  "comment": "22 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study conditions on automorphisms of Boolean algebras of the form $P(\\lambda)/I_\\kappa$ (where $\\lambda$ is an uncountable cardinal and $I_\\kappa$ is the ideal of sets of cardinality less than $\\kappa$) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every cardinality-preserving automorphism of $P(2^\\kappa)/I_{\\kappa^+}$ which is trivial on all sets of cardinality $\\kappa^+$ is trivial, and that $MA_{\\aleph_1}$ implies that every automorphism of $P(\\mathbb{R})/Fin$ is trivial on a cocountable set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-10T19:39:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35"
    ],
    "keywords": [
      "boolean algebras",
      "study conditions",
      "uncountable cardinal",
      "cardinality-preserving automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150603433L"
    }
  }
}