{
  "id": "1504.02805",
  "version": "v1",
  "published": "2015-04-10T22:22:30.000Z",
  "updated": "2015-04-10T22:22:30.000Z",
  "title": "DNR and incomparable Turing degrees",
  "authors": [
    "Mingzhong Cai",
    "Noam Greenberg",
    "Michael McInerney"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We construct an increasing $\\omega$-sequence $(a_n)$ of Turing degrees which forms an initial segment of the Turing degrees, and such that each~$a_{n+1}$ is diagonally noncomputable relative to $a_n$. It follows that the~$\\mathsf{DNR}$ principle of reverse mathematics does not imply the existence of Turing incomparable degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-10T22:22:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D28"
    ],
    "keywords": [
      "incomparable turing degrees",
      "initial segment",
      "reverse mathematics",
      "turing incomparable degrees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150402805C"
    }
  }
}