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Finite Spectra of Syllogistic Logic with Cardinality Comparisons — arXiv:2609.24902

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.24902
License (as archived): CC0-1.0
Archived: 2026-10-09T21:57:58.110Z
SHA-256 of the archived text: 8e0fe7a375a4ab846bf20bbecfaf0a3ab42a0b5466ffddf454d9f800c0fd0cf9
Stable URL of this page: https://metraipolis.com/documento/dc_ee44ea8e80cd

How to cite

Finite Spectra of Syllogistic Logic with Cardinality Comparisons — arXiv:2609.24902 — arXiv (en), https://arxiv.org/abs/2609.24902 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ee44ea8e80cd (Metraipolis archive dc_ee44ea8e80cd, sha256 8e0fe7a375a4ab846bf20bbecfaf0a3ab42a0b5466ffddf454d9f800c0fd0cf9)

BibTeX

@misc{dcee44ea8e80cd,
  title = {Finite Spectra of Syllogistic Logic with Cardinality Comparisons — arXiv:2609.24902},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.24902},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ee44ea8e80cd; sha256 8e0fe7a375a4ab846bf20bbecfaf0a3ab42a0b5466ffddf454d9f800c0fd0cf9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.24902. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\Gamma$, namely the set of positive integers $n$ for which $\Gamma$ 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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-22 in math.LO).
Categorie arXiv: Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2609.24902 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T21:44:20.591Z dalla pagina https://arxiv.org/catchup/math.LO/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).