Definable Categorical Equivalence.

This article proposes to explicate theoretical equivalence by supplementing formal equivalence criteria with preservation conditions concerning interpretation. I argue that both the internal structure of models and choices of morphisms are aspects of formalisms that are relevant when it comes to their interpretation. Hence, a formal criterion suitable for being supplemented with preservation conditions concerning interpretation should take these two aspects into account. The two currently most important criteria—generalized definitional equivalence (Morita equivalence) and categorical equivalence—are not optimal in this respect. I put forward a criterion that takes both aspects into account: the criterion of definable categorical equivalence. [ABSTRACT FROM AUTHOR]