Truth and infinity
Rudolf v.B. Rucker · Proceedings of the American Mathematical Society · 1976
This paper formalizes Gödel’s 1946 conjecture that every set-theoretic sentence is decidable from the present axioms plus some true axioms of infinity; and we prove a weak variant of this conjecture to be true for every ZF {\text {ZF}} universe. We then make precise the extent to which unbound quantifiers can be taken to range only over ordinals in ZF {\text {ZF}} , obtaining a sort of normal-form theorem. The last section relates these results to the problem of how wide the class of all sets is.