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An Introduction to Proof Theory – Normalization, Cut-Elimination, and Consistency Proofs - Oxford Scholarship Online
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An Introduction to Proof Theory: Normalization, Cut-Elimination, and Consistency Proofs

Paolo Mancosu, Sergio Galvan, and Richard Zach

Abstract

Proof theory is a central area of mathematical logic of special interest to philosophy. It has its roots in the foundational debate of the 1920s, in particular, in Hilbert’s program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, “finitary” means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results ... More

Keywords: proof theory, consistency proof, proof transformation, ordinal notation, inductive proof, formalization of mathematics, philosophy of mathematics, Hilbert’s program, Gerhard Gentzen

Bibliographic Information

Print publication date: 2021 Print ISBN-13: 9780192895936
Published to Oxford Scholarship Online: October 2021 DOI:10.1093/oso/9780192895936.001.0001

Authors

Affiliations are at time of print publication.

Paolo Mancosu, author
Willis S. and Marion Slusser Professor of Philosophy, University of California at Berkeley

Sergio Galvan, author
Emeritus Professor of Logic, Catholic University of Milan

Richard Zach, author
Professor of Philosophy, University of Calgary