Here Carnap describes not the language but rather what is to be done with the language. This consists of definitions of the following:

• rules of formation (syntactic)
• rules of relative designation (these give tbe designation of some phrase of the language relative to some model and value assignment)
• rules of direct designation (which gives a model for the language)
• definition of truth (a sentence is true if it designates truth in the model given by the rules of direct designation according to the rules of relative designation)
• meaning postulates (these are axioms which express relations between the descriptive constants)

A model is said to be admissible if all the meaning postulates hold in it.

Analyticity (A-truth) is then defined as follows:

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.