Related papers: Priestley-style duality for filter-distributive co…
We introduce a general framework for generating dualities between categories of partial orders and categories of ordered Stone spaces; we recover in particular the classical Priestley duality for distributive lattices and establish several…
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…
This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures dually…
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier foundational work of such authors as Nachbin,…
We characterize Priestley spaces of algebraic, arithmetic, coherent, and Stone frames. As a corollary, we derive the well-known dual equivalences in pointfree topology involving various categories of algebraic frames.
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a…
The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour…
The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
There are several prominent duality results in pointfree topology. The Hofmann-Lawson duality establishes that the category of continuous frames is dually equivalent to the category of locally compact sober spaces. This restricts to a dual…
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms…
In this paper we study the class of modules with fusion and implication based over distributive lattices, or FIDL-modules, for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and…
We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between…
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…
In this paper, we investigate a bitopological duality for algebras of Fitting's multi-valued logic. We also extend the natural duality theory for $\mathbb{ISP_I}(\mathcal{L})$ by developing a duality for $\mathbb{ISP}(\mathcal{L})$, where…
Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global…