{
  "id": "1602.03784",
  "version": "v1",
  "published": "2016-02-11T16:27:54.000Z",
  "updated": "2016-02-11T16:27:54.000Z",
  "title": "$\\mathsf{RT}_2^2$ does not imply $\\mathsf{WKL}_0$",
  "authors": [
    "Lu Liu"
  ],
  "comment": "12 pages",
  "journal": "Journal of Symbolic Logic, 2012, 77(2): 609",
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that $\\mathsf{RCA}_0+\\mathsf{RT}_2^2\\not\\rightarrow \\mathsf{WKL}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\\bar{A}$, such that $G\\oplus C$ is also not of PA-degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-11T16:27:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F35",
      "03C62",
      "03D30",
      "03D80"
    ],
    "keywords": [
      "infinite subset"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203784L"
    }
  }
}