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

  • Book
  • © 2014

Overview

Authors:
  1. Anna Horská

    1. Department of Logic, Charles University in Prague, Czech Republic

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  • 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)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Anna Horská
    Pages 1-9

  3. Preliminaries

    • Anna Horská
    Pages 11-28

  4. Ordinal Numbers

    • Anna Horská
    Pages 29-40

  5. Consistency Proof

    • Anna Horská
    Pages 41-69

  6. Back Matter

    Pages 71-77
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Keywords

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)

Authors and Affiliations

  • Department of Logic, Charles University in Prague, Czech Republic

    Anna Horská

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

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