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A note on Sugihara algebras.

Josep M. Font;  Gonzalo Rodríguez Pérez — 1992

Publicacions Matemàtiques

In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of Sugihara algebras. Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same...

Wajsberg algebras.

Josep M. Font;  Antonio J. Rodríguez;  Antoni Torrens — 1984

Stochastica

We present the basic theory of the most natural algebraic counterpart of the ℵ-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....

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