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GENTZEN’S OVERVIEW OF CALCULI AND REDUCTIONS IN CONSISTENCY PROOFS

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  11 November 2025

JAN VON PLATO
JAN VON PLATO*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HELSINKI, FINLAND 00014 HELSINKI, FINLAND
*
E-mail: jan.vonplato@helsinki.fi
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Abstract

Gentzen’s sequent calculi were a part of his consistency program, the ultimate aim of which was a proof of the consistency of analysis. Among Gentzen’s series of shorthand notes there was one titled WKR in which various sequent calculi and cut elimination procedures are examined. Nothing of this series has survived, but there is instead a late summary Gentzen wrote of it in 1944. In this article, these calculi and reductions are described in the context of Gentzen’s consistency program, followed by an English translation of his manuscript that is written in what is known as the unified German shorthand (einheitliche Kurzschrift).

Keywords

Gentzencut eliminationconsistency proofs

MSC classification

Primary: 03F03: Proof theory, general 03F05: Cut-elimination and normal-form theorems

Information

Type
Article
Information
Bulletin of Symbolic Logic , Volume 31 , Issue 3 , September 2025 , pp. 385 - 417
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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