{
  "id": "1704.07678",
  "version": "v1",
  "published": "2017-04-20T21:21:20.000Z",
  "updated": "2017-04-20T21:21:20.000Z",
  "title": "Provability Logics of Hierarchies",
  "authors": [
    "Amirhossein Akbar Tabatabai"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The branch of provability logic investigates the provability-based behavior of the mathematical theories. In a more precise way, it studies the relation between a mathematical theory $T$ and a modal logic $L$ via the provability interpretation which interprets the modality as the provability predicate of $T$. In this paper we will extend this relation to investigate the provability-based behavior of a hierarchy of theories. More precisely, using the modal language with infinitely many modalities, $\\{\\Box_n\\}_{n=0}^{\\infty}$, we will define the hierarchical counterparts of some of the classical modal theories such as $\\mathbf{K4}$, $\\mathbf{KD4}$, $\\mathbf{GL}$ and $\\mathbf{S4}$. Then we will define their canonical provability interpretations and their corresponding soundness-completeness theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-20T21:21:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "provability logic",
      "provability-based behavior",
      "mathematical theory",
      "canonical provability interpretations",
      "provability predicate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}