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 sense to the calculus R of relevance logic, and we determine the totally ordered, the subdirectly irreducible, and the simple members of this variety, by using some consequences of the algebraizability of the logic RM (R-Mingle) with which they are associated.
@article{urn:eudml:doc:41736,
title = {A note on Sugihara algebras.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {591-599},
mrnumber = {MR1209825},
zbl = {0781.03052},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41736}
}
Font, Josep M.; Rodríguez Pérez, Gonzalo. A note on Sugihara algebras.. Publicacions Matemàtiques, Tome 36 (1992) pp. 591-599. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41736/