Functional Monadic Bounded Algebras.


The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions.

We show that FMBA is characterised by the disjunction of the equations E =1 and E =0. We also define a weaker notion of ``relatively functional'' algebra, and show that every member of MBA is isomorphic to a relatively functional one.