{
  "id": "math/0609022",
  "version": "v2",
  "published": "2006-09-01T10:08:53.000Z",
  "updated": "2007-02-21T09:15:29.000Z",
  "title": "Interval orders and reverse mathematics",
  "authors": [
    "Alberto Marcone"
  ],
  "comment": "21 pages; to appear in Notre Dame Journal of Formal Logic; minor changes from the previous version",
  "journal": "Notre Dame Journal of Formal Logic 48 (2007), 425-448",
  "doi": "10.1305/ndjfl/1187031412",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain $2 \\oplus 2$. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it contains neither $2 \\oplus 2$ nor $3 \\oplus 1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-21T09:15:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B30",
      "06A06",
      "03D45"
    ],
    "keywords": [
      "reverse mathematics",
      "study proper interval orders",
      "characterization theorem",
      "partial order",
      "implications"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9022M"
    }
  }
}