 Here the labels are the addition symbol ‘+’, the minus symbol ‘\(-\)’ and the constant symbol ‘0’. An interpretation also needs to specify a domain for the quantifiers. With one proviso, the models of this set of sentences are precisely the structures that mathematicians know as abelian groups. The proviso is that in an abelian group \(A\), the domain should contain the interpretation of the symbol 0, and it should be closed under the interpretations of the symbols + and \(-\). In mathematical model theory one builds this condition (or the corresponding conditions for other function and constant symbols) into the definition of a structure. 