{
  "id": "1804.09451",
  "version": "v1",
  "published": "2018-04-25T09:42:52.000Z",
  "updated": "2018-04-25T09:42:52.000Z",
  "title": "Provability Logic and the Completeness Principle",
  "authors": [
    "Albert Visser",
    "Jetze Zoethout"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\\Box$ and $\\triangle$ that prove the schemes $A\\to\\triangle A$ and $\\Box\\triangle S\\to\\Box S$ for $S\\in\\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\\Sigma_1$-provability logic of Heyting Arithmetic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T09:42:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F45",
      "03F50",
      "03F55"
    ],
    "keywords": [
      "provability logic",
      "completeness principle",
      "intuitionistic theories",
      "provability predicates",
      "mojtaba mojtahedi"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}