{
  "id": "1703.02588",
  "version": "v1",
  "published": "2017-03-07T20:47:05.000Z",
  "updated": "2017-03-07T20:47:05.000Z",
  "title": "Fixed Points of Self-embeddings of Models of Arithmetic",
  "authors": [
    "Saeideh Bahrami",
    "Ali Enayat"
  ],
  "comment": "35 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate the structure of fixed point sets of self-embeddings of models of arithmetic. In particular, given a countable nonstandard model M of a modest fragment of Peano arithimetic, we provide complete characterizations of (a) the initial segments of M that can be realized as the longest initial segment of fixed points of a nontrivial self-embedding of M onto a proper initial segment of M; and (b) the initial segments of M that can be realized as the fixed point set of some nontrivial self-embedding of M onto a proper initial segement of M. Moreover, we demonstrate the the standard cut is strong in M iff there is a self-embedding of M onto a proper initial segment of itself that moves every element that is not definable in M by an existential formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-07T20:47:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F30",
      "03C62",
      "03H15",
      "03C15"
    ],
    "keywords": [
      "proper initial segment",
      "arithmetic",
      "fixed point set",
      "longest initial segment",
      "proper initial segement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}