Abstract
BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.
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The preliminary research for this paper was carried out while the second author was visiting Salerno University. The second author would like to thank the first author and Salerno University for their hospitality. The second author acknowledges partial supports from Salerno University and from the belgian Fonds National de la Recherche Scientifique.
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Nola, A., Niederkorn, P. Natural dualities for varieties of BL-algebras. Arch. Math. Logic 44, 995–1007 (2005). https://doi.org/10.1007/s00153-005-0312-0
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DOI: https://doi.org/10.1007/s00153-005-0312-0