{
  "abstract": "Suppose that L is a quantum logic (= an orthomodular poset) and A, B are Boolean subalgebras of L. Suppose further that s1(resp. s2) is a state on A (resp. on B). We ask when both s1 and s2 allow for a simultaneous extension over L. Under a natural necessity condition on A, B, s1, s2 we find a sufficient condition for the existence of the extension. This condition is the requirement of an abundance of two-valued states on L. We then show by the Greechie pasting technique that this condition is far from necessary even for state-space-rich logics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10770",
  "author_total": 3,
  "authors": [
    {
      "name": "Dominika Burešová"
    },
    {
      "name": "Pavel Pták"
    },
    {
      "name": "Jan Ševic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2v6tg327wnqkp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10770",
  "fulltext_url": null,
  "id": "2v6tg327wnqkp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10770",
  "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.LO"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7212259223",
  "pdf_url": "https://arxiv.org/pdf/2609.10770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2v6tg327wnqkp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10770"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Simultaneous extensions of states on quantum logics",
  "title_text": "Simultaneous extensions of states on quantum logics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/2v6tg327wnqkp",
  "venue": "arXiv",
  "versions": []
}