Natural Duality as a Tool to Study Algebras Arising from Logics
MV-algebras are the algebraic counterpart of Lukasiewicz’s infinite-valued logic, just as Boolean algebras correspond to the classical propositional calculus. The finitely generated subvarieties of the variety M of all MV-algebras are generated by a finite number of finite chains.
We present Davey and Werner’s theory of natural duality, illustrated by its application to a few classes of algebras arising from classical and non-classical logics. We insist on the subvarieties of M generated by one finite chain, for which some simple applications of the dualities are proposed.
KeywordsBoolean Algebra Free Algebra Natural Duality Strong Duality Unary Relation
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