{
  "annotation_id": "dbcd4c81-5422-4096-b974-406e48e14d1f",
  "date_created": "2026-02-17T05:53:12.051000Z",
  "date_modified": "2026-02-17T05:53:12.051000Z",
  "file_hash": "41a5f86ef5ea0d606d41316360139d22f337240e95085267591d9d879155cdb4",
  "private": false,
  "record": {
    "abstract": "This paper provides an extensive study of the $\\mathscr{I}$-Miller null ideals $M_\\mathscr{I}$, $\\sigma$-ideals on the Baire space parametrized by ideals $\\mathscr{I}$ on countable sets. These $\\sigma$-ideals are associated to the idealized versions of Miller forcing in the same way that the meager ideal is associated to Cohen forcing. We compute the cardinal invariants of $M_\\mathscr{I}$ for typical examples of Borel ideals $\\mathscr{I}$ and show that Cicho\\\u0027{n}\u0027s Maximum can be extended by adding the uniformity and covering numbers of $M_\\mathscr{I}$ for different ideals $\\mathscr{I}$.",
    "arxiv_id": "2601.07428",
    "authors": [
      "Aleksander Cie\u015blak",
      "Takehiko Gappo",
      "Arturo Mart\u00ednez-Celis",
      "Takashi Yamazoe"
    ],
    "categories": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Cardinal invariants of idealized Miller null sets",
    "url": "https://arxiv.org/abs/2601.07428",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "014b0966-f670-4ae3-a408-801de79be755",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}