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Notre Dame Journal of Formal Logic

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

Osamu Takaki

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

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.

Primary Subjects: 03F05
Secondary Subjects: 03F10
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1039700743
Mathematical Reviews number (MathSciNet): MR1624946
Digital Object Identifier: doi:10.1305/ndjfl/1039700743
Zentralblatt MATH identifier: 0937.03067

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