| Résume | An interpretation between theories can be presented as a composition of the construction of imaginary sorts, and the taking of reducts. In this work with Michael Benedikt, we consider more general ways of reducing structure, using definable equivalence relations on models with a given universe or, equivalently as it turns out, definable groupoids extending the groupoid of models and isomorphisms. We characterize the simplest ones from several points of view; continuous logic turns out surprisingly to play an intrinsic role. Examples seem to hint at a possibility of contact with categories that are usually inaccessible to definability considerations, notably from differential geometry. This is a preliminary investigation, and I hope to be able to give complete proofs of the main results. |
