  We affirm a conjecture of Sacks [1972] by showing that every countable
distributive lattice is isomorphic to an initial segment of the hyperdegrees,
$\mathcal{D}_{h}$. In fact, we prove that every sublattice of any
hyperarithmetic lattice (and so, in particular, every countable locally finite
lattice) is isomorphic to an initial segment of $\mathcal{D}_{h}$. Corollaries
include the decidability of the two quantifier theory of $% \mathcal{D}_{h}$
and the undecidability of its three quantifier theory. The key tool in the
proof is a new lattice representation theorem that provides a notion of forcing
for which we can prove a version of the fusion lemma in the hyperarithmetic
setting and so the preservation of $\omega _{1}^{CK}$. Somewhat surprisingly,
the set theoretic analog of this forcing does not preserve $\omega _{1}$. On
the other hand, we construct countable lattices that are not isomorphic to an
initial segment of $\mathcal{D}_{h}$.
