Notre Dame Journal of Formal Logic

Strong Normalization Theorem for a Constructive Arithmetic with Definition by Transfinite Recursion and Bar Induction

Osamu Takaki

Abstract

We prove the strong normalization theorem for the natural deduction system for the constructive arithmetic TRDB (the system with Definition by Transfinite Recursion and Bar induction), which was introduced by Yasugi and Hayashi. We also establish the consistency of this system, applying the strong normalization theorem.

Article information

Source
Notre Dame J. Formal Logic, Volume 38, Number 3 (1997), 350-373.

Dates
First available in Project Euclid: 12 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1039700743

Digital Object Identifier
doi:10.1305/ndjfl/1039700743

Mathematical Reviews number (MathSciNet)
MR1624946

Zentralblatt MATH identifier
0937.03067

Subjects
Primary: 03F05: Cut-elimination and normal-form theorems
Secondary: 03F10: Functionals in proof theory

Citation

Takaki, Osamu. Strong Normalization Theorem for a Constructive Arithmetic with Definition by Transfinite Recursion and Bar Induction. Notre Dame J. Formal Logic 38 (1997), no. 3, 350--373. doi:10.1305/ndjfl/1039700743. https://projecteuclid.org/euclid.ndjfl/1039700743


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References

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