{
  "id": "2401.00572",
  "version": "v1",
  "published": "2023-12-31T19:19:17.000Z",
  "updated": "2023-12-31T19:19:17.000Z",
  "title": "Sealed Kurepa Trees",
  "authors": [
    "Itamar Giron",
    "Yair Hayut"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small forcing notion which adds a branch to it without collapsing cardinals. On the other hand, we derive a proper forcing notion for making an arbitrary Kurepa tree into a non-distributive tree without collapsing $\\aleph_1$ and $\\aleph_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-31T19:19:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E35"
    ],
    "keywords": [
      "sealed kurepa trees",
      "arbitrary kurepa tree",
      "proper forcing notion",
      "small forcing notion",
      "collapsing cardinals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}