Strictly as presented in PM, however, the no-classes theory differs significantly from ZF. The sentences of the PM theory are expressed in the theory of types, as opposed to the first order theory of ZF. ZF and PM cannot simply be compared in terms of their theorems. Not only are there different axioms in the two theories, but the very languages in which they are expressed differ in logical power. If we follow Gödel and Boolos, however, the two are seen to be based on the same intuitive basis, a