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An Introduction to Proof Theory: Normalization, Cut-Elimination, and Consistency

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Book Title
An Introduction to Proof Theory: Normalization, Cut-Elimination,
Publication Date
2021-08-17
ISBN
9780192895936
Publication Year
2021
Type
Textbook
Format
Hardcover
Language
English
Publication Name
Introduction to Proof Theory : Normalization, Cut-Elimination, and Consistency Proofs
Item Height
9.4in
Author
Paolo Mancosu, Sergio Galvan, Richard Zach
Item Length
1in
Publisher
Oxford University Press, Incorporated
Item Width
6.3in
Item Weight
28.1 Oz
Number of Pages
432 Pages

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Product Information

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 Gödel-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.

Product Identifiers

Publisher
Oxford University Press, Incorporated
ISBN-10
0192895931
ISBN-13
9780192895936
eBay Product ID (ePID)
7050032472

Product Key Features

Author
Paolo Mancosu, Sergio Galvan, Richard Zach
Publication Name
Introduction to Proof Theory : Normalization, Cut-Elimination, and Consistency Proofs
Format
Hardcover
Language
English
Publication Year
2021
Type
Textbook
Number of Pages
432 Pages

Dimensions

Item Length
1in
Item Height
9.4in
Item Width
6.3in
Item Weight
28.1 Oz

Additional Product Features

Lc Classification Number
Qa9.54
Table of Content
Preface1 Introduction2 Axiomatic calculi3 Natural deduction4 Normal deductions5 The sequent calculus6 The cut-elimination theorem7 The consistency of arithmetic8 Constructive ordinals and induction9 The consistency of arithmetic, continuedAppendices:A The Greek alphabetB Set-theoretic notationC Axioms, rules, and theorems of axiomatic calculiD Exercises on axiomatic derivationsE Natural deductionF Sequent calculusG Outline of the cut elimination theorem
Topic
General
Lccn
2021-910782
Dewey Decimal
511.36
Intended Audience
Scholarly & Professional
Dewey Edition
23
Illustrated
Yes
Genre
Mathematics, Philosophy

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