Localic Priestley duality

Priestley Duality for Bilattices

We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices a...

Fine hierarchies via Priestley duality

Priestley duality for N4-lattices

We present a new Priestley-style topological duality for bounded N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that for our topological ...

A non-commutative Priestley duality

We prove that the category of left-handed skew distributive lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a noncommutative version of classical Priestley duality for distributive lattices. The result also generalizes the recent development of Stone duality for skew Boolean algebras.

Priestley Duality for Strong Proximity Lattices

In 1937 Marshall Stone extended his celebrated representation theorem for Boolean algebras to distributive lattices. In modern terminology, the representing topological spaces are zero-dimensional stably compact, but typically not Hausdorff. In 1970, Hilary Priestley realised that Stone’s topology could be enriched to yield orderdisconnected compact ordered spaces. In the present paper, we gene...