II. Models, model structures and interpretations

Carnap's terminology differs here from the terminology which I am accustomed to.

In my usage an interpretation is an assignment of values to the domains of quantification and the contants in some language
(the details depend upon the kind of language under consideration), a model is an interpretation which satisfies the axioms
of the theory.

In Carnap's usage a model is what I call an interpretation, a model structure is an isomorphism class of models. and an interpretation
is some kind of definition of a model so that two distinct interpretations might describe the same model.
Two interpretations are the same if they are logically equivalent.