Duality theory for enriched Priestley spaces

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...

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 ...

Descent for Priestley Spaces

A characterization of descent morphism in the category of Priestley spaces, as well as necessary and sufficient conditions for such morphisms to be effective are given. For that we embed this category in suitable categories of preordered topological spaces were descent and effective morphisms are described using the monadic description of descent.

Fine hierarchies via Priestley duality

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...