This work is a step toward the development of a logic for types and computation that
includes not only the usual spaces of mathematics and constructions, but also spaces from
logic and domain theory. Using realizability, we investigate a configuration of three toposes
that we regard as describing a notion of relative computability. Attention is focussed on a
certain local map of toposes, which we first study axiomatically, and then by deriving a
modal calculus as its internal logic. The resulting framework is intended as a setting for the
logical and categorical study of relative computability.