Feferman proved that, on a certain reconstruction, the predicativist theory does not prove any new arithmetical statements beyond those provable in Peano Arithmetic

An intermediate position is that defended by classical “predicativists” such as Poincaré and Weyl. The theory, presented in a satisfactory logical way by Feferman and others, accepts the excluded middle on the natural numbers (and as such it is arguably committed to the existence of the set of natural numbers and in any case to accepting bivalence on the natural numbers) but does not accept the existence of the power set of the natural numbers. According to predicativism (see Feferman 2005), set