Applications of Priestley duality in transferring optimal dualities

Abstract

This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety $$\mathbb{I}\mathbb{S}\mathbb{P}(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{4} )$$ of Kleene algebras and the quasi-varieties $$B$$ n of pseudocomplemented distributive lattices (n ≥ 1).