  We use a way to extend partial combinatory algebras (pcas) by forcing them to
represent certain functions. In the case of Scott's Graph model, equality is
computable relative to the complement function. However, the converse is not
true. This creates a hierarchy of pcas which relates to similar structures of
extensions on other pcas. We study one such structure on Kleene's second model
and one on a pca equivalent but not isomorphic to it. For the recursively
enumerable sub pca of the Graph model, results differ as we can compute the
(partial) complement function using the equality.
