Locally Finite Quasivarieties of MV-algebras
@article{Gispert2014LocallyFQ,
title={Locally Finite Quasivarieties of MV-algebras},
author={Joan Gispert and Antoni Torrens},
journal={arXiv: Logic},
year={2014}
}In this paper we show that every locally finite quasivariety of MV-algebras is finitely generated and finitely based. To see this result we study critical MV-algebras. We also give axiomatizations of some of these quasivarieties.
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References
SHOWING 1-10 OF 22 REFERENCES
Equational characterization of all varieties of MV-algebras
- Mathematics
- 1999
Abstract It is known that all subvarieties of MV -algebras are finitely axiomatizable. In the literature, one can find equational characterizations of certain subvarieties, such as MV n -algebras. In…
Varieties of MV-algebras
- MathematicsJ. Appl. Non Class. Logics
- 1999
For every subvariety V of the variety of all MV- algebras, the free objects in V are characterized and the results are used to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.
Cyclic Elements in MV-Algebras and Post Algebras
- MathematicsMath. Log. Q.
- 1994
In this paper, cyclic elements in MV-algebras are studied which are the generators of the fundamental chain of the Post algebra.
Congruence distributive quasivarieties whose finitely subdirectly irreducible members form a universal class
- Mathematics
- 1990
By a congruence distributive quasivariety we mean any quasivarietyK of algebras having the property that the lattices of those congruences of members ofK which determine quotient algebras belonging…
On subquasivariety lattices of semi-primal varieties
- Mathematics
- 1985
be an algebra with the operations defined as follows: for all x, y, x---~y = rain {1, 1 x + y} and -~x = 1 x. This algebra is due to Jan YLukasiewicz. Applying McNaughton 's criterion f rom [3] we…
Algebraic analysis of many valued logics
- Mathematics
- 1958
This paper is an attempt at developing a theory of algebraic systems that would correspond in a natural fashion to the No-valued propositional calculus(2). For want of a better name, we shall call…
A new proof of the completeness of the Łukasiewicz axioms
- Mathematics
- 1959
The purpose of this note is to provide a new proof for the completeness of the Lukasiewicz axioms for infinite valued propositional logic. For the existing proof of completeness and a history of the…
Un Estudio algebraico de los cálculos proposicionales de Lukasiewicz
- Philosophy
- 1980
TRAS UNA BREVE PRESENTACION DE LAS ALGEBRAS DE SALES
ASOCIADAS A LA PARTE IMPLICATIVA DEL CALCULO
PROPOSICIONAL INFINITO VALENTE DE LUKASIEWICZ SE
ESTUDIAN LAS PROPIEDADES LOGICO-ALGEBRAICAS MAS…