发表机构
The University of Notre Dame（圣母大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对带基数比较的三段论逻辑$S^\dagger(card)$的有限谱给出完全分类，并证明加入句子级布尔连接词后，其谱集构成由原谱生成的拓扑。
AI 中文摘要
我们研究了带基数比较的三段论逻辑$S^\dagger(card)$的有限谱。由于该语言在句子层面不包含合取，我们考虑理论$\Gamma$的谱，即使得$\Gamma$在$n$元模型上可满足的正整数$n$的集合。我们给出了这些谱的完全分类：除空集外，每个$S^\dagger(card)$-谱要么是正整数的最终尾段，要么是正偶数的最终尾段。然后我们考虑在句子层面加入布尔连接词后$S^\dagger(card)$的扩展，并证明其谱的集合构成了由原语言谱生成的拓扑。
英文摘要
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.
