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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Applications of Finite Duality to Locally Finite Varieties of BL-Algebras
verfasst von : Stefano Aguzzoli, Simone Bova, Vincenzo Marra
Erschienen in: Logical Foundations of Computer Science
Verlag: Springer Berlin Heidelberg
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We are concerned with the subvariety of commutative, bounded, and integral residuated lattices, satisfying divisibility and prelinearity, namely, BL-algebras. We give an explicit combinatorial description of the category that is dual to finite BL-algebras. Building on this, we obtain detailed structural information on the locally finite subvarieties of BL-algebras that are analogous to Grigolia’s subvarieties of finite-valued MV-algebras. As an illustration of the power of the finite duality presented here, we give an exact recursive formula for the cardinality of free finitely generated algebras in such varieties.