{
  "id": "1607.01625",
  "version": "v1",
  "published": "2016-07-06T14:05:54.000Z",
  "updated": "2016-07-06T14:05:54.000Z",
  "title": "On the set-generic multiverse",
  "authors": [
    "Sy David Friedman",
    "Sakaé Fuchino",
    "Hiroshi Sakai"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver's theorem and Bukovsk\\'y's theorem assert that set-generic extensions of a given ground model constitute a quite reasonable and sufficiently general class of standard models of set-theory. In sections 2 and 3 of this note, we give a proof of Bukovsk\\'y's theorem in a modern setting (for another proof of this theorem see Bukovsk\\'y [4]). In section 4 we check that the multiverse of set-generic extensions can be treated as a collection of countable transitive models in a conservative extension of ZFC. The last section then deals with the problem of the existence of infinitely-many independent buttons, which arose in the modal-theoretic approach to the set-generic multiverse by J.Hamkins and B.Loewe [12].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-06T14:05:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E40",
      "03E70",
      "03E99"
    ],
    "keywords": [
      "set-generic multiverse",
      "set-generic extensions",
      "infinitely-many independent buttons",
      "bukovskys theorem assert",
      "ground model constitute"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}