{
  "id": "1712.06198",
  "version": "v1",
  "published": "2017-12-17T22:41:55.000Z",
  "updated": "2017-12-17T22:41:55.000Z",
  "title": "Ultrafilter extensions do not preserve elementary equivalence",
  "authors": [
    "Denis I. Saveliev",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that there exist models $\\mathcal M_1$ and $\\mathcal M_2$ such that $\\mathcal M_1$ elementarily embeds into $\\mathcal M_2$ but their ultrafilter extensions $\\beta(\\mathcal M_1)$ and $\\beta(\\mathcal M_2)$ are not elementarily equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-17T22:41:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C55",
      "54D35",
      "54D80",
      "03C30",
      "03C80",
      "54H10"
    ],
    "keywords": [
      "preserve elementary equivalence",
      "ultrafilter extensions",
      "elementarily embeds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}