SpringerBriefs in Philosophy

Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals

Authors: Horská, Anna

  • Unique detailed explanation of the first published consistency proof of PA (peano arithmetic)
  • Includes Gentzen's unusual notation for ordinal numbers up to ε_0 and its connection to Cantor normal form
  • Probably the most important step in the history of proof theory analysed
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eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02171-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-02170-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book explains the first published consistency proof of PA. It contains the original Gentzen's proof, but it uses modern terminology and examples to illustrate the essential notions. The author comments on Gentzen's steps which are supplemented with exact calculations and parts of formal derivations. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. This representation is analysed and connection to set-theoretical representation is found, namely an algorithm for translating Gentzen's notation into Cantor normal form. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert's program and who do not mind reading mathematical texts.​

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)

Table of contents (4 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02171-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-02170-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals
Authors
Series Title
SpringerBriefs in Philosophy
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-02171-3
DOI
10.1007/978-3-319-02171-3
Softcover ISBN
978-3-319-02170-6
Series ISSN
2211-4548
Edition Number
1
Number of Pages
IX, 77
Topics