Turunen, Esko Boolean deductive systems of BL-algebras. (English) Zbl 1030.03048 Arch. Math. Logic 40, No. 6, 467-473 (2001). Summary: BL-algebras appear as Lindenbaum algebras from many-valued logic and were introduced by P. Hájek [Metamathematics of fuzzy logic. Dordrecht: Kluwer (1998; Zbl 0937.03030)]. In this paper Boolean deductive systems and implicative deductive systems of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a deductive systems \(D\) is implicative, (ii) \(D\) is Boolean, (iii) \(L/D\) is a Boolean algebra. Moreover, a BL-algebra \(L\) contains a proper Boolean deductive systems iff \(L\) is bipartite. Local BL-algebras are also characterized. These results generalize some theorems presented by C. S. Hoo for MV-algebras, which are BL-algebras fulfilling an additional double negation law \(x=x^{**}\). Cited in 1 ReviewCited in 89 Documents MSC: 03G25 Other algebras related to logic 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness 06D35 MV-algebras Citations:Zbl 0937.03030 PDFBibTeX XMLCite \textit{E. Turunen}, Arch. Math. Logic 40, No. 6, 467--473 (2001; Zbl 1030.03048) Full Text: DOI