A note on Sugihara algebras.

Font, Josep M., and Rodríguez Pérez, Gonzalo. "A note on Sugihara algebras.." Publicacions Matemàtiques 36.2A (1992): 591-599. <http://eudml.org/doc/41736>.

@article{Font1992,
abstract = {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.},
author = {Font, Josep M., Rodríguez Pérez, Gonzalo},
journal = {Publicacions Matemàtiques},
keywords = {R-Mingle; equivalent quasivariety semantics; variety of Sugihara algebras; equational base; variety of R-algebras; relevance logic; algebraizability},
language = {eng},
number = {2A},
pages = {591-599},
title = {A note on Sugihara algebras.},
url = {http://eudml.org/doc/41736},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Font, Josep M.
AU - Rodríguez Pérez, Gonzalo
TI - A note on Sugihara algebras.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2A
SP - 591
EP - 599
AB - 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.
LA - eng
KW - R-Mingle; equivalent quasivariety semantics; variety of Sugihara algebras; equational base; variety of R-algebras; relevance logic; algebraizability
UR - http://eudml.org/doc/41736
ER -