{
  "id": "2103.08702",
  "version": "v1",
  "published": "2021-03-15T20:29:19.000Z",
  "updated": "2021-03-15T20:29:19.000Z",
  "title": "Multiplicative finite embeddability vs divisibility of ultrafilters",
  "authors": [
    "Boris Šobot"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations $\\mid_M$ and $\\widetilde{\\mid}$. The set of its minimal elements proves to be very rich, and the $\\widetilde{\\mid}$-hierarchy is used to get a better intuition of this richness. We find the place of the set of $\\widetilde{\\mid}$-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets of $\\mathbb{N}$, and compare it to other such notions, important for infinite combinatorics and topological dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-15T20:29:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D35",
      "54D80",
      "11U99",
      "03E05",
      "03H15"
    ],
    "keywords": [
      "multiplicative finite embeddability",
      "infinite combinatorics",
      "minimal elements",
      "better intuition",
      "maximal ultrafilters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}