{
  "id": "1401.0648",
  "version": "v1",
  "published": "2014-01-03T13:51:02.000Z",
  "updated": "2014-01-03T13:51:02.000Z",
  "title": "The modal logic of Reverse Mathematics",
  "authors": [
    "Carl Mummert",
    "Alaeddine Saadaoui",
    "Sean Sovine"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the \"logical\" content of the implication and nonimplication relations between subsystems in Reverse Mathematics. We present a sound, complete, decidable, and compact tableau-style deductive system for s-logic, and explore in detail two fragments that are particularly relevant to Reverse Mathematics practice and automated theorem proving of Reverse Mathematics results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-03T13:51:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B30",
      "03B45"
    ],
    "keywords": [
      "modal logic",
      "reverse mathematics results",
      "compact tableau-style deductive system",
      "reverse mathematics practice",
      "implication relationship"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0648M"
    }
  }
}