Model theory is a branch of mathematical logic concerned with the study of formal theories viewed as mathematical structures or objects. Those mathematical structures are studied by examining the first order sentences that describe those structures and the sets in those structures that are defined by first order formulas. Model theory is that part of mathematics that demonstrates how to apply mathematical logic to the study of structures in mathematics. Those structures investigated in model theory can be expressed in a formal language that usually consists of first order statements.

Model theory's fundamental tools are interpretations. Mathematical truth is like all truth in that it is relative to specific situations and depends upon how and where it is interpreted. This is because of the language used to express mathematical ideas rather than to mathematics itself. The theory itself is generally one consisting of interpretations of axiomatic...