{
  "id": "1409.5699",
  "version": "v1",
  "published": "2014-09-19T15:32:44.000Z",
  "updated": "2014-09-19T15:32:44.000Z",
  "title": "The $Σ$_1 Provability Logic of HA",
  "authors": [
    "Mohammad Ardeshir",
    "S. Mojtaba Mojtahedi"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper we introduce a modal theory $H_{\\sigma}$, which is sound and complete for arithmetical $\\Sigma$_1 substitutions in ${\\bf HA}$, in other words, we will show that $H_{\\sigma}$ is the $\\Sigma$_1-provability logic of ${\\bf HA}$. Moreover we will show that $H_{\\sigma}$ is decidable. As a by-product of these results, we show that ${\\bf HA} + \\Box\\bot$ has de Jongh property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-19T15:32:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "provability logic",
      "modal theory",
      "jongh property",
      "substitutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5699A"
    }
  }
}