  The power set axiom allows us to form a set of all subsets of a given set. An example of impredicative use of power set is given by the definition of a subset of the natural numbers, \(N\), as follows: \(B := \{n \in N : \forall C \subseteq N \phi(n, C)\}\), where \(\phi\) can be taken to be a bounded formula. A form of circularity arises here as \(B\) itself is among the subsets of \(N\) which need to be checked for \(\phi\). As emphasized by Myhill (1975, 354), power set is hard to justify from a constructive point of view: it gathers together all the subsets of a given set, but does not prescribe a rule that "constructs" the set out of previously given sets, as predicativity would seem to require. 