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arXiv · 2312.10873

Bounded distributive lattices with strict implication and weak difference

Sergio Celani·Agustín Nagy·William Zuluaga Botero
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Abstract

In this paper we introduce the class of weak Heyting Brouwer algebras (WHB-algebras, for short). We extend the well known duality between distributive lattices and Priestley spaces, in order to exhibit a relational Priestley-like duality for WHB-algebras. Finally, as an application of the duality, we build the tense extension of a WHB-algebra and we employ it as a tool for proving structural properties of the variety such as the finite model property, the amalgamation property, the congruence extension property and the Maehara interpolation property.

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Sergio Celani, Agustín Nagy, William Zuluaga Botero. 2023-12-18. Bounded distributive lattices with strict implication and weak difference. https://arxiv.org/abs/2312.10873

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