 The displacement of type theory by set theory took place during the 1920s. The aim was still to unify all of mathematics, and to provide a capacious universe of abstract objects in order to do so. All the different mathematical theories would be interpretable within set theory, upon suitable identification of ‘set-theoretic surrogates’ for the objects studied by those theories. So, for example, the finite von Neumann ordinals can serve as set-theoretic surrogates for the natural  numbers.[27]  And ℘(ω), the power set of the set of natural numbers, is the set-theoretic surrogate for the real  continuum.[28] 