The Priestley duality for Wajsberg algebras (Q753812)

Wajsberg algebras are the algebraic counterpart of Łukasiewicz logic that is defined with axioms which characterize implication and negation and with Modus Ponens as a rule [\textit{A. J. Rodriguez}, Un estudio algebraico de los cálculos proposicionales de Łukasiewicz. Ph. D. Thesis, Univ. Barcelona (1980)]. In this paper, Wajsberg algebras are considered as Kleene algebras and bounded distributive lattices. The aim of this paper is to develop a duality theory for Wajsberg algebras, extending the duality between Kleene algebras and some ordered topological spaces that is considered by \textit{W. Cornish} and \textit{P. Fowler} [J. Austral. Math. Soc., Ser. A 27, 209-220 (1978; Zbl 0403.06010)]. A Wajsberg space is characterized as Kleene space over a family of partial functions satisfying a number of algebraic and topological properties.