Definition:Mathematical Theory

A mathematical theory, or just theory, is a concept in mathematical logic.

It consists of a series of sentences in a formal system.

Bourbaki Definition
The definition according to Bourbaki's is as follows:

The signs of a mathematical theory $$\mathcal{T}$$ are:
 * 1) The logical signs: $$\Box, \tau, \vee, \rceil$$.
 * 2) The letters: uppercase and lowercase Roman letters, with or without accents, e.g. $$A, A', A''$$.
 * 3) The specific signs which depend on the theory under consideration.

A mathematical theory also contains:
 * a series of rules which lets us determine whether particular assemblies are either terms or relations of the theory;
 * another series of rules which lets us determine whether particular assemblies are theorems of the theory.