{
  "id": "0801.1912",
  "version": "v1",
  "published": "2008-01-12T18:04:52.000Z",
  "updated": "2008-01-12T18:04:52.000Z",
  "title": "Large cardinals and gap-1 morasses",
  "authors": [
    "Andrew D. Brooke-Taylor",
    "Sy-David Friedman"
  ],
  "comment": "49 pages",
  "journal": "Annals of Pure and Applied Logic 159, no. 1-2 (2009), pp 71-99",
  "doi": "10.1016/j.apal.2008.10.007",
  "categories": [
    "math.LO"
  ],
  "abstract": "We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular uncountable cardinal, while preserving all n-superstrong (0<n<omega+1), hyperstrong and 1-extendible cardinals. In the latter case, a preliminary forcing to make the GCH hold is required. Our forcing yields morasses that satisfy an extra property related to the homogeneity of the partial order; we refer to them as mangroves and prove that their existence is equivalent to the existence of morasses. Finally, we exhibit a partial order that forces universal morasses to exist at every regular uncountable cardinal, and use this to show that universal morasses are consistent with n-superstrong, hyperstrong, and 1-extendible cardinals. This all contributes to the second author's outer model programme, the aim of which is to show that L-like principles can hold in outer models which nevertheless contain large cardinals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-12T18:04:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55"
    ],
    "keywords": [
      "partial order",
      "second authors outer model programme",
      "regular uncountable cardinal",
      "reverse easton iteration",
      "forces universal morasses"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}