{
  "id": "2404.03315",
  "version": "v1",
  "published": "2024-04-04T09:23:51.000Z",
  "updated": "2024-04-04T09:23:51.000Z",
  "title": "The complexity of non-stationary ideals",
  "authors": [
    "Philipp Lücke"
  ],
  "comment": "Survey paper. 26 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We present an overview of results on the question of whether the non-stationary ideal of an uncountable regular cardinal $\\kappa$ can be defined by a $\\Pi_1$-formula using parameters of hereditary cardinality at most $\\kappa$. These results show that this question is deeply connected to several central topics of current research in set theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-04T09:23:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E47",
      "03E05",
      "03E35",
      "03E45"
    ],
    "keywords": [
      "non-stationary ideal",
      "complexity",
      "uncountable regular cardinal",
      "set theory",
      "hereditary cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}