正则Heyting代数的Esakia对偶

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2023-11-21 DOI:10.1007/s00012-023-00833-5

Gianluca Grilletti, Davide Emilio Quadrellaro

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引用次数: 1

摘要

本文利用Esakia对偶研究了正则Heyting代数。特别地，我们给出了正则Heyting代数对偶的Esakia空间的一个刻画，并证明了由正则Heyting代数生成的Heyting代数存在连续多变种。我们还研究了这类对象的几种逻辑应用，并利用它们为探究逻辑、\(\texttt{DNA}\) -逻辑和依赖逻辑提供了新的拓扑完备性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Esakia duals of regular Heyting algebras

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Esakia duals of regular Heyting algebras

We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we give a characterisation of Esakia spaces dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, \(\texttt{DNA}\)-logics and dependence logic.

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来源期刊

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.