{
  "id": "2402.11616",
  "version": "v2",
  "published": "2024-02-18T15:16:24.000Z",
  "updated": "2024-08-29T08:45:19.000Z",
  "title": "Conservation of Ramsey's theorem for pairs and well-foundedness",
  "authors": [
    "Quentin Le Houérou",
    "Ludovic Levy Patey",
    "Keita Yokoyama"
  ],
  "comment": "36 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this article, we prove that Ramsey's theorem for pairs and two colors is $\\Pi^1_1$-conservative over~$\\mathsf{RCA}_0 + \\mathsf{B}\\Sigma^0_2 + \\mathsf{WF}(\\epsilon_0)$ and over~$\\mathsf{RCA}_0 + \\mathsf{B}\\Sigma^0_2 + \\bigcup_n \\mathsf{WF}(\\omega^\\omega_n)$. These results improve theorems from Chong, Slaman and Yang and Ko{\\l}odziejczyk and Yokoyama and belong to a long line of research towards the characterization of the first-order part of Ramsey's theorem for pairs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-08-29T08:45:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramseys theorem",
      "conservation",
      "well-foundedness",
      "long line",
      "first-order part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}