Locally Finite Quasivarieties of MV-algebras
Joan Gispert, Antoni Torrens
TL;DR
This paper proves that all locally finite quasivarieties of MV-algebras are finitely generated and based, providing axiomatizations and analyzing critical MV-algebras to establish these foundational properties.
Contribution
It establishes that every locally finite quasivariety of MV-algebras is finitely generated and finitely based, advancing the algebraic theory of MV-algebras.
Findings
Locally finite quasivarieties of MV-algebras are finitely generated.
Such quasivarieties are also finitely based.
Axiomatizations are provided for some quasivarieties.
Abstract
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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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge