Effective model theory vs. recursive model theory

Recursive model theory is supposed to be the study of the effectiveness of constructions and theorems in model theory. This often involves getting «effective» versions of various classical model-theoretic notions. We suggest a new approach to studying the effectiveness of model theory, an approach we have dubbed «effective model theory». The basic idea is to allow arbitrary nonrecursive models, but to require all notions to be relativized to the complexity of the models involved. For example we have an effective model theory version of the property of being intrinsically r.e.