Particularly important are those definable sets that are also substructures, i. e. contain all constants and are closed under function application. For instance, one can study the definable subgroups of a certain group. However, there is no need to limit oneself to substructures in the same signature. Since formulas with n free variables define subsets of , n-ary relations can also be definable. Functions are definable if the function graph is a definable relation, and constants are definable if there is a formula such that a is the only element of such that is true. In this way, one can study definable groups and fields in general structures, for instance, which has been important in geometric stability theory.
Particularly important are those definable sets that are also substructures, i. e. contain all constants and are closed under function application For instance, one can study the definable subgroups of a certain group. However, there is no need to limit oneself to substructures in the same signature. Since formulas with n free variables define subsets of , n-ary relations can also be definable. Functions are definable if the function graph is a definable relation, and constants are definable if there is a formula such that a is the only element of such that is true. In this way, one can study definable groups and fields in general structures, for instance, which has been important in geometric stability theory.