{
  "id": "2405.17101",
  "version": "v1",
  "published": "2024-05-27T12:21:31.000Z",
  "updated": "2024-05-27T12:21:31.000Z",
  "title": "Ultrafilter extensions of bounded graphs are elementary",
  "authors": [
    "Zalán Molnár"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The main motivation of this paper is the study of first-order model theoretic properties of structures having their roots in modal logic. We will focus on the connections between ultrafilter extensions and ultrapowers. We show that certain structures (called bounded graphs) are elementary substructures of their ultrafilter extensions, moreover their modal logics coincide.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-27T12:21:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ultrafilter extensions",
      "bounded graphs",
      "first-order model theoretic properties",
      "modal logics coincide",
      "main motivation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}