Consistency proof via pointwise induction

Archive for Mathematical Logic 37 (3):149-165 (1998)

Abstract

We show that the consistency of the first order arithmetic $PA$ follows from the pointwise induction up to the Howard ordinal. Our proof differs from U. Schmerl [Sc]: We do not need Girard's Hierarchy Comparison Theorem. A modification on the ordinal assignment to proofs by Gentzen and Takeuti [T] is made so that one step reduction on proofs exactly corresponds to the stepping down $\alpha\mapsto\alpha [1]$ in ordinals. Also a generalization to theories $ID_q$ of finitely iterated inductive definitions is proved

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References found in this work

A New System of Proof-Theoretic Ordinal Functions.W. Buchholz - 1986 - Annals of Pure and Applied Logic 32:195-207.

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