  Computability relative to a partial function $f$ on the natural numbers can
be formalized using the notion of an oracle for this function $f$. This can be
generalized to arbitrary partial combinatory algebras, yielding a notion of
`adjoining a partial function to a partial combinatory algebra $A$'. A similar
construction is known for second-order functionals, but the third-order case is
more difficult. In this paper, we prove several results for this third-order
case. Given a third-order functional $\Phi$ on a partial combinatory algebra
$A$, we show how to construct a partial combinatory algebra $A[\Phi]$ where
$\Phi$ is `computable', and which has a `lax' factorization property. Moreover,
we show that, on the level of first-order functions, the effect of making a
third-order functional computable can be described as adding an oracle for a
first-order function.
