What word to use to describe the mathematical objects and axioms of a branch of math I'm trying to write a paragraph which describes the objects and rules of a branch of mathematics. But I'm stuck as to what word I should use here.  
Example: (fill the blank)
Arithmetic is an example of a  mathematical ____ that is defined in terms of the objects it uses (numbers and operations) and a finite number of rules (or axioms) which are true statements about the ____.
At the moment I'm just using 'system' because I don't know what else to use but I'm not sure this is a good word or if there is a more formal term.

In a slightly different context, the word Structure would be a good fit. Learn about mathematical structures here. 
Otherwise, System is a reasonably good fit. In a slightly different context, theory might also be appropriate, as Henning Makholm suggested.
