  Chevalley's theorem on the images of morphisms of schemes and the principle
of quantifier elimination for the theory of algebraically closed fields are
widely understood to be two perspectives on the same theorem. In this paper, we
demonstrate that both results can easily be proven simultaneously, using a
mixture of geometric and logical techniques. In doing so, we give logical
meaning to geometric points of schemes and to finitely presented morphisms
thereof, in a manner reminiscent of Spencer Breiner's logical schemes.
