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

Makoto Kikuchi and Kazuyuki Tanaka
Source: Notre Dame J. Formal Logic Volume 35, Number 3 (1994), 403-412.

#### 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.

First Page:
Primary Subjects: 03F35
Secondary Subjects: 03F30
Full-text: Open access

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

### References

[1] Boolos, G., A new proof of the Gödel Incompleteness Theorem," Notices of the American Mathematical Society, vol. 36 (1989), pp. 388--390.
Zentralblatt MATH: 0972.03544
[2] Feferman, S., Arithmetization of metamathematics in a general setting," Fundamenta Mathematicae, vol. 49 (1960), pp. 35--92.
Mathematical Reviews (MathSciNet): MR26:4913
Zentralblatt MATH: 0095.24301
[3] Kikuchi, M., A note on Boolos' proof of the Incompleteness Theorem," Mathematical Logic Quarterly, vol. 40 (1994), pp. 528--532.
Mathematical Reviews (MathSciNet): MR95j:03095
Zentralblatt MATH: 0805.03052
Digital Object Identifier: doi:10.1002/malq.19940400409
[4] Kreisel, G., Notes on arithmetical models for consistent formulae of the predicate calculus," Fundamenta Mathematicae, vol. 37 (1950), pp. 265--285.
Mathematical Reviews (MathSciNet): MR12,790a
Zentralblatt MATH: 0040.00302
[5] Simpson, S., Subsystems of Second Order Arithmetic, forthcoming.
Mathematical Reviews (MathSciNet): MR2001i:03126
Zentralblatt MATH: 0909.03048
[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.
Mathematical Reviews (MathSciNet): MR457132