论弱海廷代数的蕴涵-最小子项

Pub Date : 2024-07-06 DOI:10.1002/malq.202300021
Sergio Celani, Hernán J. San Martín
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引用次数: 0

摘要

弱海廷代数(weak Heyting algebras)的种类是由 Celani 和 Jansana 于 2005 年提出的。它对应于正常模态逻辑的严格蕴涵片段,也被称为所有克里普克模型类的亚直觉局部后果。亚残差格是海廷格的广义化,也是弱海廷格的特例。它们是由爱泼斯坦和霍恩在 20 世纪 70 年代引入的,作为卢伊和哈金之前研究的一些强蕴涵逻辑的代数对应物。在本文中,我们将研究弱海廷代数的蕴涵-最小子项类。特别是,我们通过给出等式基来证明该类是一个综类。我们还提出了一个代数范畴的拓扑对偶性,其对象是亚残差格的蕴涵-非极大子归结。
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On the implicative-infimum subreducts of weak Heyting algebras

The variety of weak Heyting algebras was introduced in 2005 by Celani and Jansana. This corresponds to the strict implication fragment of the normal modal logic K $K$ which is also known as the subintuitionistic local consequence of the class of all Kripke models. Subresiduated lattices are a generalization of Heyting algebras and particular cases of weak Heyting algebras. They were introduced during the 1970s by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. In this paper we study the class of implicative-infimum subreducts of weak Heyting algebras. In particular, we prove that this class is a variety by giving an equational base for it. We also present a topological duality for the algebraic category whose objects are the implicative-infimum subreducts of subresiduated lattices.

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