Notre Dame Journal of Formal Logic

On Formalization of Model-Theoretic Proofs of Gödel's Theorems

Abstract

Within a weak subsystem of second-order arithmetic $WKL_{0}$, that is $\Pi^0_2$-conservative over $PRA$, we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

Article information

Source
Notre Dame J. Formal Logic, Volume 35, Number 3 (1994), 403-412.

Dates
First available in Project Euclid: 21 December 2002

https://projecteuclid.org/euclid.ndjfl/1040511346

Digital Object Identifier
doi:10.1305/ndjfl/1040511346

Mathematical Reviews number (MathSciNet)
MR1326122

Zentralblatt MATH identifier
0822.03032

Citation

Kikuchi, Makoto; Tanaka, Kazuyuki. On Formalization of Model-Theoretic Proofs of Gödel's Theorems. Notre Dame J. Formal Logic 35 (1994), no. 3, 403--412. doi:10.1305/ndjfl/1040511346. https://projecteuclid.org/euclid.ndjfl/1040511346

References

• Boolos, G., “A new proof of the Gödel Incompleteness Theorem," Notices of the American Mathematical Society, vol. 36 (1989), pp. 388–390. Zbl 0972.03544
• Feferman, S., “Arithmetization of metamathematics in a general setting," Fundamenta Mathematicae, vol. 49 (1960), pp. 35–92. Zbl 0095.24301 MR 26:4913
• Kikuchi, M., “A note on Boolos' proof of the Incompleteness Theorem," Mathematical Logic Quarterly, vol. 40 (1994), pp. 528–532. Zbl 0805.03052 MR 95j:03095
• Kreisel, G., “Notes on arithmetical models for consistent formulae of the predicate calculus," Fundamenta Mathematicae, vol. 37 (1950), pp. 265–285. Zbl 0040.00302 MR 12,790a
• Simpson, S., Subsystems of Second Order Arithmetic, forthcoming. Zbl 0909.03048 MR 2001i:03126
• Simpson, S., and K. Tanaka, “On the strong soundness of the theory of real closed fields," Proceedings of the Fourth Asian Logic Conference, (1990), pp. 7–10.
• Smoryński, C., “The Incompleteness Theorems," pp. 821–865 in Handbook of Mathematical Logic, edited by J. Barwise, North Holland, Amsterdam, 1977.