Boolean deductive systems of BL-algebras

Archive for Mathematical Logic 40 (6):467-473 (2001)
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Abstract

BL-algebras rise as Lindenbaum algebras from many valued logic introduced by Hájek [2]. In this paper Boolean ds and implicative ds of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a ds D is implicative, (ii) D is Boolean, (iii) L/D is a Boolean algebra. Moreover, a BL-algebra L contains a proper Boolean ds iff L is bipartite. Local BL-algebras, too, are characterized. These results generalize some theorems presented in [4], [5], [6] for MV-algebras which are BL-algebras fulfiling an additional double negation law x = x **

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Citations of this work

Subdirectly irreducible state-morphism BL-algebras.Anatolij Dvurečenskij - 2011 - Archive for Mathematical Logic 50 (1-2):145-160.
Some results in BL ‐algebras.Arsham Borumand Saeid & Somayeh Motamed - 2009 - Mathematical Logic Quarterly 55 (6):649-658.
On (∈, ∈ ∨ q)‐fuzzy filters of R0‐algebras.Xueling Ma, Jianming Zhan & Young B. Jun - 2009 - Mathematical Logic Quarterly 55 (5):493-508.
Hyper-Archimedean BL-algebras are MV-algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
On -fuzzy filters ofR0-algebras.Xueling Ma, Jianming Zhan & Young B. Jun - 2009 - Mathematical Logic Quarterly 55 (5):493-508.

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