2024/10/31 by Guram Bezhanishvili, Bezhanishvili, Guram, Ramón Jansana +1
Computer Science · #06A12 #06D20 #06D50 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2410.23664
openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new duality for distributive and implicative meet semi-lattices. For distributive meet semi-lattices our duality generalizes Priestley's duality for distributive lattices and provides an improvement of Celani's duality. Our generalized Priestley spaces are similar to the ones constructed by Hansoul. Thus, one can view our duality for distributive meet semi-lattices as a completion of Hansoul's work. For implicative meet semi-lattices our duality generalizes Esakia's duality for Heyting algebras and provides an improvement of Vrancken-Mawet's and Celani's dualities. In the finite case it also yield's Köhler's duality. Thus, one can view our duality for implicative meet semi-lattices as a completion of Köhler's work. As a consequence, we also obtain a new duality for Heyting algebras, which is an alternative to the Esakia duality.