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Algebraic functions in Łukasiewicz implication algebras
(World Scientific, 2016-03)
In this article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on ...
Free Łukasiewicz implication algebras
(Springer, 2008-06)
Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper ...
Decomposability of free Łukasiewicz implication algebras
(Springer, 2006-11)
Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127-133, 1978. ...
Implicative subreducts of MV-algebras: free and weakly projective objects
(Birkhauser Verlag Ag, 2017-12)
In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions ...
Topological representation for monadic implication algebras
(De Gruyter, 2009-01-17)
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic ...
Topological representation for implication algebras
(Birkhauser Verlag Ag, 2004-11)
In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of ...
Variations of the free implicative semilattice extension of a Hilbert algebra
(Springer Verlag Berlín, 2019-07)
Celani and Jansana (Math Log Q 58(3):188–207, 2012) give an explicit description of the free implicative semilattice extension of a Hilbert algebra. In this paper, we give an alternative path conducing to this construction. ...
Monadic MV-algebras II: Monadic implicational subreducts
(Springer, 2014-03)
In this paper, we study the class of all monadic implicational subreducts, that is, the {→, ∀, 1}-subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ML, and ...
Zariski-type topology for implication algebras
(Wiley VCH Verlag, 2010-06)
In this work we provide a new topological representation for implication algebras in such a way that its one- point compactification is the topological space given in [1]. Some applications are given thereof.