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.

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

Inhalt

Acknowledgements.- 1 Introduction.- 2 Preliminaries.- 3 Ordinal numbers.- 4 Consistency proof.- Index.- References.