{
  "id": "1404.3703",
  "version": "v1",
  "published": "2014-04-14T19:21:53.000Z",
  "updated": "2014-04-14T19:21:53.000Z",
  "title": "Coherent ultrafilters and nonhomogeneity",
  "authors": [
    "Jan Starý"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "We introduce the notion of a coherent $P$-ultrafilter on a complete ccc Boolean algebra, strenghtening the notion of a $P$-point on $\\omega$, and show that these ultrafilters exist generically under ${\\mathfrak c} = {\\mathfrak d}$. This improves the known existence result of Ketonen. Similarly, the existence theorem of Canjar can be extended to show that coherently selective ultrafilters exist generically under ${\\mathfrak c} = {cov(M)}$. We use these ultrafilters in a topological application: a coherent $P$-ultrafilter on an algebra $B$ is an untouchable point in the Stone space of $B$, witnessing its nonhomogeneity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-14T19:21:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54G05",
      "06E10"
    ],
    "keywords": [
      "coherent ultrafilters",
      "nonhomogeneity",
      "complete ccc boolean algebra",
      "existence theorem",
      "stone space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3703S"
    }
  }
}