Metatheory

The study of the inner structure of a mathematical theory considered as a whole. It deals with the general properties of the rules according to which the objects of a certain theory are combined and linked, and the principles of reasoning on which its argumentation is based. When describing the language of the theory, the metatheory must resort to a different language located on a higher level, since the terms and symbols of the theory are looked at from above, as objects to be described and related. For this reason, this new language is often called a metalanguage.