Bounded distributive lattices with strict implication and weak difference
Logic
2023-12-19 v1 Category Theory
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.
Cite
@article{arxiv.2312.10873,
title = {Bounded distributive lattices with strict implication and weak difference},
author = {Sergio Celani and Agustín Nagy and William Zuluaga Botero},
journal= {arXiv preprint arXiv:2312.10873},
year = {2023}
}