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.