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. "
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