{
  "id": "1405.2558",
  "version": "v1",
  "published": "2014-05-11T18:00:48.000Z",
  "updated": "2014-05-11T18:00:48.000Z",
  "title": "On a Hierarchy of Reflection Principles in Peano Arithmetic",
  "authors": [
    "Elena Nogina"
  ],
  "comment": "13 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study reflection principles of Peano Arithmetic PA which are based on both proof and provability. Any such reflection principle in PA is equivalent to either $\\Box P\\!\\rightarrow\\! P$ ($\\Box P$ stands for `$P$ is provable') or $\\Box^k u\\!\\!:\\!\\!P\\!\\rightarrow\\! P$ for some $k\\geq 0$ ($t:P$ states `$t$ is a proof of $P$'). Reflection principles constitute a non-collapsing hierarchy with respect to their deductive strength $$u\\!\\!:\\!\\!P\\!\\rightarrow\\! P\\ \\ \\prec\\ \\ \\Box u\\!\\!:\\!\\!P\\!\\rightarrow\\! P\\ \\ \\prec\\ \\ \\Box^2 u\\!\\!:\\!\\!P\\!\\rightarrow\\! P \\ \\ \\prec\\ \\ldots\\ \\prec\\ \\ \\Box P\\!\\rightarrow\\! P.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-11T18:00:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F03",
      "03F25",
      "03F30",
      "03F45"
    ],
    "keywords": [
      "study reflection principles",
      "peano arithmetic pa",
      "reflection principles constitute",
      "equivalent",
      "non-collapsing hierarchy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2558N"
    }
  }
}