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The Priestley duality for Wajsberg algebras. (English) Zbl 0717.03026
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 [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 W. Cornish and 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.
Reviewer: G.E.Tseytlin

MSC:
03G25 Other algebras related to logic
03B50 Many-valued logic
06F30 Ordered topological structures
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References:
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