Truth and infinity
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- by R. v. B. Rucker PDF
- Proc. Amer. Math. Soc. 59 (1976), 138-143 Request permission
Abstract:
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 ${\text {ZF}}$ universe. We then make precise the extent to which unbound quantifiers can be taken to range only over ordinals in ${\text {ZF}}$, 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.References
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K. Gödel, Remarks before the Princeton Bicentennial Conference on Problems in Mathematics, 1946, The Undecidable, M. Davis (editor), Raven Press, Hewlett, N.Y., 1965, pp. 84-88.
R. Rucker, Truth and infinity, Notices Amer. Math. Soc. 20 (1973), A-444. Abstract #73TE45.
—, On Cantor’s continuum problem (to appear).
- G. Takeuti, Formalization principle, Logic, Methodology and Philos. Sci. III (Proc. Third Internat. Congr., Amsterdam, 1967) North-Holland, Amsterdam, 1968, pp. 105–118. MR 0252220
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 138-143
- MSC: Primary 02K15; Secondary 02A05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0424565-5
- MathSciNet review: 0424565