Construction of monadic three-valued Łukasiewicz algebras (Q1189898)

A monadic three-valued Łukasiewicz algebra is a three-valued Łukasiewicz algebra with an existential quantifier, and it generalizes the notion of monadic Boolean algebra. Two distinct existential quantifiers \(\exists\) and \(\exists^*\) on a Boolean algebra \(B\) are said to commute if \(\exists\forall^* x=\forall^*\exists x\) (where \(\forall^* x=-\exists^*-x\)) for all \(x\in B\). Let \(B\) be a Boolean algebra and let \(\exists\) and \(\exists^*\) be two existential quantifiers defined on \(B\) that commute. In this paper the authors show how this can be used to construct a monadic three-valued Łukasiewicz algebra. They also characterize all commuting existential quantifiers on a finite Boolean algebra. As a second construction the authors construct a monadic three-valued Łukasiewicz algebra from a monadic Boolean algebra \(B\) and a monadic ideal \(I\) of \(B\).