{
  "id": "1406.2084",
  "version": "v2",
  "published": "2014-06-09T06:09:34.000Z",
  "updated": "2015-03-18T06:22:44.000Z",
  "title": "Spectra of Tukey types of ultrafilters on Boolean algebras",
  "authors": [
    "Jennifer A. Brown",
    "Natasha Dobrinen"
  ],
  "comment": "18 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Extending recent investigations on the structure of Tukey types of ultrafilters on $\\mathcal{P}(\\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras, including interval algebras, tree algebras, and pseudo-tree algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-09T06:09:34.000Z",
      "abstract": "Extending recent investigations on the structure of Tukey types of ultrafilters on $\\mathcal{P}(\\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras. These include the classes of free Boolean algebras, superatomic Boolean algebras generated by almost disjoint families, interval algebras, tree algebras, and pseudo-tree algebras. We also give conditions guaranteeing the existence of an ultrafilter of maximum Tukey type, and show that each free algebra has exactly one Tukey type, the maximum.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-18T06:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06E05",
      "03G05",
      "06A07",
      "03E04"
    ],
    "keywords": [
      "ultrafilter",
      "free boolean algebras",
      "maximum tukey type",
      "disjoint families",
      "superatomic boolean algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.2084B"
    }
  }
}