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An Introduction to Proof Theory

An Introduction to Proof Theory

Normalization, Cut-Elimination, and Consistency Proofs

by Paolo MancosuSergio Galvan and Richard Zach
Paperback
Publication Date: 01/08/2021
 
An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Goedel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction
and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal
notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
ISBN:
9780192895943
9780192895943
Category:
Philosophy
Format:
Paperback
Publication Date:
01-08-2021
Publisher:
Oxford University Press
Country of origin:
United Kingdom
Pages:
432
Dimensions (mm):
234x156mm

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