Boolean products of BL-algebras
BL algebras are the Lindenbaum algebras of Hájek's Basic Logic. As shown in \textit{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.
Lindenbaum algebras of Hájek's Basic Logic
scientific article; zbMATH DE number 1545038