# A note on Sugihara algebras.

Josep M. Font; Gonzalo Rodríguez Pérez

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 2A, page 591-599
- ISSN: 0214-1493

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topFont, 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 -