{
  "abstract": "Banakh and Bazylevych introduced separation-axiom variants $\\mathfrak q_i$, for $i=1,2,2\\frac{1}{2}$, of the cardinal $\\mathfrak q$, together with a cardinal $\\mathfrak{adp}$ lying between $\\mathfrak{dp}$ and $\\mathfrak{ap}$. They asked whether $\\mathfrak{adp}$ coincides with either of these two cardinals. We prove in ZFC that $\\mathfrak{adp}=\\mathfrak{dp}$. We define a dual variant $\\mathfrak{adp}_2$ and show that $\\mathfrak{adp}_2=\\mathfrak{ap}$. We further study the relation between $\\mathfrak{ap}$ and the weakened $Q$-space cardinals. We introduce a tree analogue $\\mathfrak{at}$ of $\\mathfrak{ap}$ and prove $\\mathfrak{at}=\\mathfrak q_{2}$, concluding that $\\mathfrak{ap}\\leq\\mathfrak q_{2}$, which answers a question of Banakh and Bazylevych. Assuming the Generalized Continuum Hypothesis, we construct ccc forcing extensions with $\\mathfrak{ap}=ω_1<\\mathfrak{at}=\\mathfrak c$, so $\\mathfrak{ap}<\\mathfrak q_2$ is consistent with ZFC.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.11326",
  "author_total": 1,
  "authors": [
    {
      "name": "Vinicius de Oliveira Rodrigues"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fct0zmdbjgkr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.11326",
  "fulltext_url": null,
  "id": "3fct0zmdbjgkr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.11326",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7161042971",
  "pdf_url": "https://arxiv.org/pdf/2605.11326",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fct0zmdbjgkr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2605.11326",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.11326"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Almost Disjointness Principles and $Q$-Space Cardinals",
  "title_text": "Almost Disjointness Principles and Q-Space Cardinals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/3fct0zmdbjgkr",
  "venue": "arXiv",
  "versions": []
}