## 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 , that is -conservative over , 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

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1040511346

Mathematical Reviews number (MathSciNet)
MR1326122

Digital Object Identifier
doi:10.1305/ndjfl/1040511346

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

#### References

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• [2] Feferman, S., Arithmetization of metamathematics in a general setting," Fundamenta Mathematicae, vol. 49 (1960), pp. 35--92.
• [3] Kikuchi, M., A note on Boolos' proof of the Incompleteness Theorem," Mathematical Logic Quarterly, vol. 40 (1994), pp. 528--532.
• [4] Kreisel, G., Notes on arithmetical models for consistent formulae of the predicate calculus," Fundamenta Mathematicae, vol. 37 (1950), pp. 265--285.
• [5] Simpson, S., Subsystems of Second Order Arithmetic, forthcoming.
• [6] 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.
• [7] Smoryński, C., The Incompleteness Theorems," pp. 821--865 in Handbook of Mathematical Logic, edited by J. Barwise, North Holland, Amsterdam, 1977.