{
  "abstract": "We study the finite spectra of the syllogistic logic with cardinality comparisons $S^\\dagger(card)$. Since the language does not contain conjunction at the sentence level, we consider the spectrum of a theory $Γ$, namely the set of positive integers $n$ for which $Γ$ is satisfiable in an $n$-element model. We give a complete classification of these spectra: besides the empty set, every $S^\\dagger(card)$-spectrum is either an eventual tail of the positive integers or an eventual tail of the positive even integers. We then consider the extension of $S^\\dagger(card)$ by Boolean connectives at the sentence level and show that the collection of its spectra forms the topology generated by the spectra of the original language.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24902",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruiting Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04v5v0ayx7e74.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24902",
  "fulltext_url": null,
  "id": "04v5v0ayx7e74",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24902",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214041070",
  "pdf_url": "https://arxiv.org/pdf/2609.24902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04v5v0ayx7e74.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Finite Spectra of Syllogistic Logic with Cardinality Comparisons",
  "title_text": "Finite Spectra of Syllogistic Logic with Cardinality Comparisons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/04v5v0ayx7e74",
  "venue": "arXiv",
  "versions": []
}