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An Introduction to Proof Theory: Normalization, Cut-Eliminatio
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eBay item number:364506895439
Item specifics
- Condition
- Book Title
- An Introduction to Proof Theory: Normalization, Cut-Elimination,
- Publication Date
- 2021-08-17
- ISBN
- 9780192895936
- Subject Area
- Mathematics, Philosophy
- Publication Name
- Introduction to Proof Theory : Normalization, Cut-Elimination, and Consistency Proofs
- Publisher
- Oxford University Press, Incorporated
- Item Length
- 1 in
- Subject
- General
- Publication Year
- 2021
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 9.4 in
- Item Weight
- 28.1 Oz
- Item Width
- 6.3 in
- Number of Pages
- 432 Pages
About this product
Product Identifiers
Publisher
Oxford University Press, Incorporated
ISBN-10
0192895931
ISBN-13
9780192895936
eBay Product ID (ePID)
7050032472
Product Key Features
Number of Pages
432 Pages
Language
English
Publication Name
Introduction to Proof Theory : Normalization, Cut-Elimination, and Consistency Proofs
Publication Year
2021
Subject
General
Type
Textbook
Subject Area
Mathematics, Philosophy
Format
Hardcover
Dimensions
Item Height
9.4 in
Item Weight
28.1 Oz
Item Length
1 in
Item Width
6.3 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2021-910782
Reviews
This book deals with the main concerns in proof theory in the first third of the 20th century. A culmination of research in this area at that time was Gerhard Gentzen's work, in particular, his papers on natural deduction, on sequent calculi and on the proof of the consistency of arithmetic... The authors of the book under review incorporate the results of some of these developments in the text (or mention them in footnotes)., "This book deals with the main concerns in proof theory in the first third of the 20th century. A culmination of research in this area at that time was Gerhard Gentzen's work, in particular, his papers on natural deduction, on sequent calculi and on the proof of the consistency of arithmetic... The authors of the book under review incorporate the results of some of these developments in the text (or mention them in footnotes)." -- Katalin Bimbo, MathSciNet
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
511.36
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
Synopsis
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., 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.
LC Classification Number
QA9.54
ebay_catalog_id
4
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eBay item number:364506895439
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