A Duality for theta-Valued Lukasiewicz-Moisil Algebras and Applications
Philosophical problems arising from the idea that there are statements which are neither true nor false. led to the formulation of many valued logics by Lukasiewtcz Since then, plenty of research has been developed in this area In 1968, Gr.C. Moisil found an example which gave him the motivation he had been looking for in order to legitimate the introduction and study of infinitely valued Lukasiewicz algebras. so he defined theta-valued Lukasiewiez algebras. where theta is the order type of a chain In this article, we determine a topological duality for theta-valued Lukasiewicz Moisil algebras (or LM(theta)-algebras) equivalent to the one given by A Filipoiu in 1980 Not only does the duality enable us to obtain a description of the LM(theta)-congruences on an LM(theta)-algebra, but also to characterize the subchrectly irreducible LM(theta)-algebras. Furthermore, we extend the above study to the case of LM(theta) -algebras with negation arriving through a different method at the results indicated by V Boiceseu et al (Lukasiewicz Moisil Algebras. Annals of Discrete Mathematics 49, North Holland, 1991)
theta-valued lukasiewicz-moisil algebras topological dualities congruences subdirectly irreducible algebras