{
  "id": "2104.09150",
  "version": "v1",
  "published": "2021-04-19T09:17:10.000Z",
  "updated": "2021-04-19T09:17:10.000Z",
  "title": "A guessing principle from a Souslin tree, with applications to topology",
  "authors": [
    "Assaf Rinot",
    "Roy Shalev"
  ],
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "We introduce a new combinatoiral principle which we call $\\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out de Caux type constructions of topological spaces. Our main result states that strong instances of $\\clubsuit_{AD}$ follow from the existence of a Souslin tree. It is also shown that the weakest instance of $\\clubsuit_{AD}$ does not follow from the existence of an almost Souslin tree. As an application, we obtain a simple, de Caux type proof of Rudin's result that if there is a Souslin tree, then there is an $S$-space which is Dowker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-19T09:17:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "54G20",
      "03E35",
      "03E65"
    ],
    "keywords": [
      "souslin tree",
      "guessing principle",
      "application",
      "caux type proof",
      "caux type constructions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}