Notre Dame Journal of Formal Logic

Reverse Mathematics and Completeness Theorems for Intuitionistic Logic

Takeshi Yamazaki

Abstract

In this paper, we investigate the logical strength of completeness theorems for intuitionistic logic along the program of reverse mathematics. Among others we show that $\sf {ACA}_0$ is equivalent over $\sf {RCA}_0$ to the strong completeness theorem for intuitionistic logic: any countable theory of intuitionistic predicate logic can be characterized by a single Kripke model.

Article information

Source
Notre Dame J. Formal Logic, Volume 42, Number 3 (2001), 143-148.

Dates
First available in Project Euclid: 12 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1063372197

Digital Object Identifier
doi:10.1305/ndjfl/1063372197

Mathematical Reviews number (MathSciNet)
MR2010178

Zentralblatt MATH identifier
1036.03008

Citation

Yamazaki, Takeshi. Reverse Mathematics and Completeness Theorems for Intuitionistic Logic. Notre Dame J. Formal Logic 42 (2001), no. 3, 143--148. doi:10.1305/ndjfl/1063372197. https://projecteuclid.org/euclid.ndjfl/1063372197

References

• Gabbay, D. M., Semantical Investigations in Heyting's Intuitionistic Logic, vol. 148 of Synthese Library, D. Reidel Publishing Company, Dordrecht, 1981.
• Ishihara, H., B. Khoussainov, and A. Nerode, "Decidable K"ripke models of intuitionistic theories, Annals of Pure and Applied Logic, vol. 93 (1998), pp. 115–23.
• Simpson, S. G., Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.
• Troelstra, A. S., and D. van Dalen, Constructivism in Mathematics. Vol. I, vol. 121 of Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, 1988.