{
  "id": "1612.04494",
  "version": "v1",
  "published": "2016-12-14T05:37:16.000Z",
  "updated": "2016-12-14T05:37:16.000Z",
  "title": "Determinacy and Fast-growing Sequences of Turing Degrees",
  "authors": [
    "Dmytro Taranovsky"
  ],
  "comment": "6 pages; see ancillary files for the original MathJax/html",
  "categories": [
    "math.LO"
  ],
  "abstract": "We discuss sufficiently fast-growing sequences of Turing degrees. The key result is that, assuming sufficient determinacy, if $\\phi$ is a formula with one free variable, and S and T are sufficiently fast-growing sequences of Turing degrees of length $\\omega_1$, then $\\phi(S) \\iff \\phi(T)$. We also define degrees for subsets of $\\omega_1$ analogous to Turing degrees, and prove that under sufficient determinacy and CH, all sufficiently high degrees are also effectively indistinguishable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-14T05:37:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E60"
    ],
    "keywords": [
      "turing degrees",
      "sufficiently fast-growing sequences",
      "define degrees",
      "sufficiently high degrees",
      "assuming sufficient determinacy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}