Duality theory emerged from the work by Marshall Stone [18] on Boolean algebras and distributive lattices in the 1930s. Later in the early 1970s Larisa Maksimova [10, 11] and Hilary Priestley [15, 16] developed analogous results for Heyting algebras, topological Boolean algebras, and distributive lattices. Duality for bounded, not necessarily distributive lattices, was developed by Alstir Urquh...

We provide new insights into the relationship between different constructions of the canonical extension of a bounded lattice. This follows on from the recent construction of the canonical extension using Ploščica’s maximal partial maps into the two-element set by Craig, Haviar and Priestley (2012). We show how this complete lattice of maps is isomorphic to the stable sets of Urquhart’s represe...

Barker, N. W., Nygaard, K. K., Walters, W., and Priestley, J. T. (1940). Proc. Mayo Clin., 15, 769. -~ ~~ (1941). Ibid., 16, 1. Browse, N. (1964). Brit. med. 7., 1, 669. Cosgriff, S. W. (1947). Amer. 7. Med., 3, 740. Felder, D. A. (1949). Surg. Gynec. Obstet., 88, 337. Gibbs, N. M. (1957). Brit. 7. Surg., 45, 209. Homans, J. (1934). New Engl. 7. Med., 211, 993. (1947). Ibid., 236, 196. Pilcher,...

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we sho...

In 2001, an open question that was posed by Blyth, Silva and Varlet in [2] is the following: for an Ockham algebra L determine the congruences on L that are kernels of endomorphisms on L. Whereas a general solution to this is stll an open problem, there has been some progress in investigating kernels of endomorphisms in various lattice-ordered algebras. In this connection, an algebra A is said ...

The variety of RDP-algebras forms the algebraic semantics of RDPlogic, the many-valued propositional logic of the revised drastic product left-continuous triangular norm and its residual. We prove a Priestley duality for finite RDP-algebras, and obtain an explicit description of coproducts of finite RDP-algebras. In this light, we give a combinatorial representation of free finitely generated R...

met with in Indian practice. The present paper is an effort to collect and expose some of the modern views, without however pretending to enter exhaustively into the subject. The ^Etiology of Glaucoma.?We may pass this heading over with but scant notice, as there is practically no difference of opinion here. All those conditions which disturb the circulation and cause congestion of the venous s...

The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that nitely-generated varieties of distributive lattices with operators are closed under canonical embedding...

We construct the exact completion for regular categories enriched in cartesian closed category Pos of partially ordered sets and monotone functions by employing a suitable calculus relations. then characterize embedding any into its use this to obtain examples concrete which arise as such completions. In particular, we prove that sense both Stone Priestley spaces is compact L. Nachbin. Finally,...