 Each mathematical structure is tied to a particular first-order language. A structure contains interpretations of certain predicate, function and constant symbols; each predicate or function symbol has a fixed arity. The collection \(K\) of these symbols is called the signature of the structure. Symbols in the signature are often called nonlogical constants, and an older name for them is primitives. The first-order language of signature \(K\) is the first-order language built up using the symbols in \(K\), together with the equality sign =, to build up its atomic formulas. (See the entry on  classical logic.)  If \(K\) is a signature, \(S\) is a sentence of the language of signature \(K\) and \(A\) is a structure whose signature is \(K\), then because the symbols match up, we know that \(A\) makes \(S\) either true or false. So one defines the class of abelian groups to be the class of all those structures of signature \(+\), \(-\), \(0\) which are models of the sentences above. Apart from the fact that it uses a formal first-order language, this is exactly the algebraists’ usual definition of the class of abelian groups; model theory formalises a kind of definition that is extremely common in mathematics.