{
  "id": "1405.2841",
  "version": "v3",
  "published": "2014-05-12T17:23:44.000Z",
  "updated": "2015-12-10T11:47:55.000Z",
  "title": "Finite Embeddability of Sets and Ultrafilters",
  "authors": [
    "Andreas Blass",
    "Mauro Di Nasso"
  ],
  "comment": "to appear in Bulletin of the Polish Academy of Sciences, Math Series",
  "categories": [
    "math.LO"
  ],
  "abstract": "A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Cech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-07T23:53:20.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-12-10T11:47:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03H15",
      "11U10"
    ],
    "keywords": [
      "natural numbers",
      "ultrafilters",
      "finite embeddability arose",
      "combinatorial number theory",
      "finite subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2841B"
    }
  }
}