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

  • Anna Horská

Part of the SpringerBriefs in Philosophy book series (BRIEFSPHILOSOPH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Anna Horská
    Pages 1-9
  3. Anna Horská
    Pages 11-28
  4. Anna Horská
    Pages 29-40
  5. Anna Horská
    Pages 41-69
  6. Back Matter
    Pages 71-77

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.​


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

Authors and affiliations

  • Anna Horská
    • 1
  1. 1.Department of LogicCharles University in PragueCzech Republic

Bibliographic information