{
  "id": "1205.2254",
  "version": "v5",
  "published": "2012-05-10T13:16:01.000Z",
  "updated": "2014-11-24T10:16:04.000Z",
  "title": "Value Groups of Real Closed Fields and Fragments of Peano Arithmetic",
  "authors": [
    "Merlin Carl",
    "Paola D'Aquino",
    "Salma Kuhlmann"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate IPA-real closed fields, that is, real closed fields which admit an integer part whose non-negative cone is a model of Peano Arithmetic. We show that the value group of an IPA-real closed field is an exponential group in the residue field. This result continues to hold for weaker fragments of Peano Arithmetic, such as $I\\Delta_{0}+EXP$. As an application, we construct a class of real closed fields which are not IPA. We classify (up to isomorphism) value groups of countable recursively saturated exponential real closed fields. We exploit this characterization to construct countable exponential real closed fields which are not IPA-real closed fields.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-01-02T13:24:21.000Z",
      "abstract": "We investigate real closed fields admitting an integer part of which non-negative cone is a model of Peano Arithmetic (or of its fragments, e.g. bounded arithmetic with exponentiation). We obtain necessary conditions on the value group of such a real closed field. These allow us to construct a class of examples of real closed fields which do not admit such integer parts",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2014-11-24T10:16:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "value group",
      "peano arithmetic",
      "integer part",
      "necessary conditions",
      "non-negative cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2254C"
    }
  }
}