{
  "id": "1310.4533",
  "version": "v1",
  "published": "2013-10-16T22:08:00.000Z",
  "updated": "2013-10-16T22:08:00.000Z",
  "title": "Ultrafilter extensions of linear orders",
  "authors": [
    "Denis I. Saveliev"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a technique allowing to obtain significant results in algebra and dynamics. Here we consider another particular case where the models are linearly ordered sets. We explicitly calculate the extensions of a given linear order and the corresponding operations of minimum and maximum on a set. We show that the extended relation is not more an order however is close to the natural linear ordering of nonempty half-cuts of the set and that the two extended operations define a skew lattice structure on the set of ultrafilters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-16T22:08:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A05",
      "03C55",
      "06B75",
      "54D80"
    ],
    "keywords": [
      "linear order",
      "ultrafilter extensions",
      "arbitrary first-order models canonically extend",
      "skew lattice structure",
      "semigroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4533S"
    }
  }
}