{
  "id": "2411.04835",
  "version": "v1",
  "published": "2024-11-07T16:20:51.000Z",
  "updated": "2024-11-07T16:20:51.000Z",
  "title": "Martin's Axiom and Weak Kurepa Hypothesis",
  "authors": [
    "Rahman Mohammadpour"
  ],
  "comment": "15 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "I show that it is consistent relative to the consistency of a Mahlo cardinal that Martin's axiom holds at $\\omega_2$, but the weak Kurepa Hypothesis fails. This answers a question posed by Honzik, Lambie-Hanson and Stejskalov\\'a. The consistency result is obtained by constructing a model where the weak Kurepa Hypothesis fails in any c.c.c. forcing extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-07T16:20:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E50",
      "03E57"
    ],
    "keywords": [
      "weak kurepa hypothesis fails",
      "martins axiom holds",
      "consistency result",
      "mahlo cardinal",
      "lambie-hanson"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}