  We examine the first order structure of pregeometries of structures built via
Hrushovski constructions. In particular, we show that the class of flat
pregeometries is an amalgamation class such that the pregeometry of the
unbounded arity Hrushovski construction is precisely its generic. We show that
the generic is saturated, provide an axiomatization for its theory, show that
the theory is $\omega$-stable, and has quantifier-elimination down to boolean
combinations of $\exists\forall$-formulas. We show that the pregeometries of
the bounded-arity Hrushovski constructions satisfy the same theory, and that
they in fact form an elementary chain.
