Constructive Sequent Reduction in Gentzen’s First Consistency Proof for Arithmetic
The purpose of this paper is to discuss Gentzen’s first consistency proof for arithmetic, the ‘galley proof’ (published for the first time in the Collected Papers, Amsterdam, 1969), by analyzing its methods of proof. Opposing positions on this subject have been taken by Bernays (1970) and Kreisel (1971). According to Kreisel’s analysis, which uses a result of Tait, it turns out that the ‘galley proof’ does not involve methods of proof exceeding transfinite induction up to ε0.
KeywordsNatural Number Reduced Form Free Variable Reduction Step Ordinal Number
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