Notre Dame Journal of Formal Logic

Reverse Mathematics and Completeness Theorems for Intuitionistic Logic

Takeshi Yamazaki


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.

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

First available: 12 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

reverse mathematics second-order arithmetic completeness theorems intuitionistic logic


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.

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