 Many syntactic operations that we are used to in first order logic work equally well in second-order logic. One such is the operation of relativization, in which we want to limit what a formula expresses to a fixed part of the universe. For example, we may consider models where a certain unary predicate U is used for the set of natural numbers. Then we relativize our axioms of arithmetic to the predicate U. Some other part of the model may be used for the power set of the set of natural numbers. Then we relativize our axioms of power set (see  §5.3)  to that part, and so on.