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We present the basic theory of the most natural algebraic counterpart of the ℵ0-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras....
In this paper we introduce and study the weakly projectable and projectable W-algebras and we review the Representation Theorem of [1].
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