{
  "id": "1410.4068",
  "version": "v1",
  "published": "2014-10-15T14:06:44.000Z",
  "updated": "2014-10-15T14:06:44.000Z",
  "title": "Separating Principles Below WKL0",
  "authors": [
    "Stephen Flood",
    "Henry Towsner"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper, we study Ramsey-type Konig's Lemma, written RWKL, using a technique introduced by Lerman, Solomon, and the second author. This technique uses iterated forcing to construct an omega-model satisfying one principle T_1 but not another T_2. The technique often allows one to translate a \"one step\" construction (building an instance of T_2 along with a collection of solutions to each computable instance of T_1) into an omega-model separation (building a computable instance of T_2 together with a Turing ideal where T_1 holds). We illustrate this translation by separating d-DNR from DNR (reproving a result of Ambos-Spies, Kjos-Hanssen, Lempp, and Slaman), and then apply this technique to separate RWKL$ from DNR (which has been shown separately by Bienvenu, Patey, and Schafer).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-15T14:06:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "separating principles",
      "study ramsey-type konigs lemma",
      "computable instance",
      "second author",
      "written rwkl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4068F"
    }
  }
}