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

2014
ISBN: 978-3-319-02170-6
Verlag: Springer International Publishing

Buch, Englisch, 77 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1474 g

Reihe: SpringerBriefs in Philosophy

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.

Zielgruppe

Research

Autoren/Hrsg.

Horská, Anna

Fachgebiete

• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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