{
  "id": "2401.14552",
  "version": "v1",
  "published": "2024-01-25T22:38:56.000Z",
  "updated": "2024-01-25T22:38:56.000Z",
  "title": "The intersection number for forcing notions",
  "authors": [
    "Andrés F. Uribe-Zapata"
  ],
  "comment": "17 pages, conference paper to appear in Proceedings of RIMS Set Theory Workshop 2023. arXiv admin note: text overlap with arXiv:2312.13443",
  "categories": [
    "math.LO"
  ],
  "abstract": "Based on works of Saharon Shelah, Jakob Kellner, and Anda T\\u{a}nasie for controlling the cardinal characteristics of the continuum in ccc forcing extensions, in the author's master's thesis was introduced a new combinatorial notion: the intersection number for forcing notions, which was used in such thesis to build a general theory of iterated forcing using finitely additive measures. In this paper, we present the definition of such a notion and prove some of its fundamental properties in detail. Additionally, we introduce a new linkedness property called $\\mu$-intersection-linked, prove some of its basic properties, and provide some interesting examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-25T22:38:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E40",
      "28A60",
      "28A12",
      "60E05",
      "06E99"
    ],
    "keywords": [
      "intersection number",
      "forcing notions",
      "authors masters thesis",
      "combinatorial notion",
      "cardinal characteristics"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}