{
  "id": "2403.09015",
  "version": "v1",
  "published": "2024-03-14T00:41:10.000Z",
  "updated": "2024-03-14T00:41:10.000Z",
  "title": "The Axiom of Choice in the $κ$-Mantle",
  "authors": [
    "Andreas Lietz"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Usuba has asked whether the $\\kappa$-mantle, the intersection of all grounds that extend to $V$ via a forcing of size ${<}\\kappa$, is always a model of ZFC. We give a negative answers by constructing counterexamples where $\\kappa$ is a Mahlo cardinal, $\\kappa=\\omega_1$ and where $\\kappa$ is the successor of a regular uncountable cardinal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-14T00:41:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E25",
      "03E35",
      "03E55"
    ],
    "keywords": [
      "mahlo cardinal",
      "regular uncountable cardinal",
      "negative answers",
      "constructing counterexamples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}