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: 12 September 2003

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

Digital Object Identifier
doi:10.1305/ndjfl/1063372197

Mathematical Reviews number (MathSciNet)
MR2010178

Zentralblatt MATH identifier
1036.03008

Subjects
Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]

Keywords
reverse mathematics second-order arithmetic completeness theorems intuitionistic logic

Citation

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


Export citation

References

  • [1] Gabbay, D. M., Semantical Investigations in Heyting's Intuitionistic Logic, vol. 148 of Synthese Library, D. Reidel Publishing Company, Dordrecht, 1981.
  • [2] Ishihara, H., B. Khoussainov, and A. Nerode, "Decidable Kripke models of intuitionistic theories", Annals of Pure and Applied Logic, vol. 93 (1998), pp. 115--23.
  • [3] Simpson, S. G., Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.
  • [4] 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.