p 算法的可解变量

arXiv - MATH - Logic Pub Date : 2024-09-13 DOI:arxiv-2409.09015

Tomasz Kowalski, Katarzyna Słomczyńska

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引用次数: 0

摘要

我们证明，对于 p 矩阵的准变量，(i) 具有可判定的一阶理论和 (ii) 有限成员具有可判定的一阶理论这两个性质是重合的。唯一具有这些性质的两个类群是三元数群和布尔代数数群。这与海廷（Heyting）代数中的情况形成了鲜明的对比，即使对于代数的变种来说，可判定的变种与有限可判定的变种也不重合。

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Decidable varieties of p-algebras

We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.

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arXiv - MATH - Logic

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