Overview
- Unique detailed explanation of the first published consistency proof of PA (peano arithmetic)
- Includes Gentzen's unusual notation for ordinal numbers up to e_0 and its connection to Cantor normal form
- Probably the most important step in the history of proof theory analysed
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Philosophy (BRIEFSPHILOSOPH)
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Table of contents (4 chapters)
Keywords
- Algorithm for translating Gentzen's notation of ordinal numbers
- Gentzen's notation and standard notation of ordinal numbers
- Gentzen's original numbering
- Gerhard Gentzen
- Hilbert's program
- Non-standard representation of ordinal numbers up to ε_0
- Ordinal numbers up to ε_0
- Peano Arithmetic
- Transfinite induction up to ε_0
About this book
Reviews
From the book reviews:
“This book deals with G. Gentzen’s classical 1936 article on the consistency of arithmetic … . The result is a clear exposition of the full proof with all details and with the ideas behind the proof visible. … All in all, the author of this book has accomplished the difficult task of making Gentzen’s original hard-to-read paper accessible to the historically interested logician.” (Christian Bennet, Mathematical Reviews, November, 2014)Authors and Affiliations
Bibliographic Information
Book Title: Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals
Authors: Anna Horská
Series Title: SpringerBriefs in Philosophy
DOI: https://doi.org/10.1007/978-3-319-02171-3
Publisher: Springer Cham
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: The Author(s) 2014
Softcover ISBN: 978-3-319-02170-6Published: 06 November 2013
eBook ISBN: 978-3-319-02171-3Published: 23 October 2013
Series ISSN: 2211-4548
Series E-ISSN: 2211-4556
Edition Number: 1
Number of Pages: IX, 77
Topics: Logic, Mathematical Logic and Foundations