Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals [electronic resource] / by Anna Horská.
By: Horská, Anna [author.].
Contributor(s): SpringerLink (Online service).
Material type:
BookSeries: SpringerBriefs in Philosophy: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: IX, 77 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319021713.Subject(s): Philosophy (General) | Logic | Logic, Symbolic and mathematical | Philosophy | Logic | Mathematical Logic and FoundationsDDC classification: 160 Online resources: Click here to access online Acknowledgements -- 1 Introduction -- 2 Preliminaries -- 3 Ordinal numbers -- 4 Consistency proof -- Index -- References.
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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