PreprintCC BY 4.0arXiv
Finite Spectra of Syllogistic Logic with Cardinality Comparisons
Abstract
We study the finite spectra of the syllogistic logic with cardinality comparisons S†(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†(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†(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.
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BibTeX
@misc{jiang2026finite,
title = {{Finite Spectra of Syllogistic Logic with Cardinality Comparisons}},
author = {Ruiting Jiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24902},
eprint = {2609.24902},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24902},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite Spectra of Syllogistic Logic with Cardinality Comparisons
AU - Ruiting Jiang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24902
UR - https://arxiv.org/abs/2609.24902
AB - We study the finite spectra of the syllogistic logic with cardinality comparisons S^†(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^†(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^†(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.
ER -