  Suppose $M$ is a countable ab-initio (uncollapsed) generic structure which is
obtained from a pre-dimension function with rational coefficients. We show that
if $H$ is a subgroup of $\mbox{Aut}\left(M\right)$ with
$\left[\mbox{Aut}\left(M\right):H\right]<2^{\aleph_{0}}$, then there exists a
finite set $A\subseteq M$ such that $\mbox{Aut}_{A}\left(M\right)\subseteq H$.
This shows that $\mbox{Aut}\left(M\right)$ has the small index property.
