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Bounded lattices with antitone involutions and properties of MV-algebras

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Chajda I., Emanovský P.

Discussiones Mathematicae - General Algebra and Applications

2004

tom 24

nr 1

31-42

We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Chajda I.

1 Emanovský P.

1 2004

Wyniki wyszukiwania

Bounded lattices with antitone involutions and properties of MV-algebras