The Iterative Hierarchy of Sets
W. W. Tait · 1990
of passing from a type A of objects to the type (PA of sets of A-objects.2 This hierarchy is essentially incompletable. For, any property of an initial segment of the stages in the hierarchy which is not possessed by some earlier segment, suffices to fix the position of a next stage in the hierarchy. This in fact is the Principle of Iteration by means of which the hierarchy is generated. But then, no such property can characterize the whole hierarchy. Note also that what we mean by a 'property' of an initial