The key to the universe is the magnificent accord between Curry-style
combinators and matching relational postulates for the semantics of a
wide range of logics. This key works most impressively in the filter
models of lambda calculus in intersection type theory developed with
Barendregt by Coppo, Dezani and the Torino school. I examine in the
present talk the degree to which the further logical modelling of
Boolean complementation can be added to this picture.