  The Posner-Robinson Theorem states that for any reals $Z$ and $A$ such that
$Z \oplus 0' \leq_\mathrm{T} A$ and $0 <_\mathrm{T} Z$, there exists $B$ such
that $A \equiv_\mathrm{T} B' \equiv_\mathrm{T} B \oplus Z \equiv_\mathrm{T} B
\oplus 0'$. Consequently, any nonzero Turing degree
$\operatorname{deg}_\mathrm{T}(Z)$ is a Turing jump relative to some $B$. Here
we prove the hyperarithmetical analog, based on an unpublished proof of Slaman,
namely that for any reals $Z$ and $A$ such that $Z \oplus \mathcal{O}
\leq_\mathrm{T} A$ and $0 <_\mathrm{HYP} Z$, there exists $B$ such that $A
\equiv_\mathrm{T} \mathcal{O}^B \equiv_\mathrm{T} B \oplus Z \equiv_\mathrm{T}
B \oplus \mathcal{O}$. As an analogous consequence, any nonhyperarithmetical
Turing degree $\operatorname{deg}_\mathrm{T}(Z)$ is a hyperjump relative to
some $B$.
