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Boolean products of BL-algebras. (English) Zbl 0966.03055

BL algebras are the Lindenbaum algebras of Hájek’s Basic Logic. As shown in P. Hájek’s book [Metamathematics of fuzzy logic, Kluwer, Dordrecht, Trends in Logic, Studia Logica Library, Vol. 4 (1998; Zbl 0937.03030)], BL algebras generalize Chang’s MV-algebras, symmetric Heyting algebras, and product algebras. They capture precisely those equational properties that are valid for all continuous “triangular norms” and their adjoint implications. The authors characterize Boolean products of BL-chains, weak Boolean products of local BL-algebras, and of perfect BL-algebras.

MSC:

03G25 Other algebras related to logic
06D35 MV-algebras

Citations:

Zbl 0937.03030
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Full Text: DOI

References:

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