{
  "id": "1607.07033",
  "version": "v1",
  "published": "2016-07-24T12:05:24.000Z",
  "updated": "2016-07-24T12:05:24.000Z",
  "title": "More notions of forcing add a Souslin tree",
  "authors": [
    "Ari Meir Brodsky",
    "Assaf Rinot"
  ],
  "comment": "15 pages. Submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "An $\\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing such a tree, Shelah proved that already the simplest forcing notion --- Cohen forcing --- adds an $\\aleph_1$-Souslin tree. In this paper, we identify a rather large class of notions of forcing that, assuming a GCH-type assumption, add a $\\lambda^+$-Souslin tree. This class includes Prikry, Magidor and Radin forcing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-24T12:05:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E35",
      "05C05"
    ],
    "keywords": [
      "souslin tree",
      "forcing add",
      "complicated combinatorial object",
      "large class",
      "simplest forcing notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}