  We show that every polynomial overring of the ring ${\rm Int}(\mathbb Z)$ of
polynomials which are integer-valued over $\mathbb Z$ may be considered as the
ring of polynomials which are integer-valued over some subset of
$\hat{\mathbb{Z}}$, the profinite completion of $\mathbb Z$ with respect to the
fundamental system of neighbourhoods of $0$ consisting of all non-zero ideals
of $\mathbb Z.$
