Notre Dame Journal of Formal Logic

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

Makoto Kikuchi and Kazuyuki Tanaka

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

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

Subjects
Primary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]
Secondary: 03F30: First-order arithmetic and fragments

Citation

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


Export citation

References

  • [1] Boolos, G., ``A new proof of the Gödel Incompleteness Theorem," Notices of the American Mathematical Society, vol. 36 (1989), pp. 388--390.
  • [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.