ENGLISH

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

By Anna Horská (auth.)

Book information

Publisher
Springer International Publishing
Year
2014
ISBN
978-3-319-02170-6, 978-3-319-02171-3
DOI
10.1007/978-3-319-02171-3
Language
english
Format
PDF
Filesize
2 MB (1795292 bytes)
Series
SpringerBriefs in Philosophy
Edition
1
Pages
77\81
Orientation
yes
Scanned
yes
Time added
2013-10-31 03:10:17
Logic; Mathematical Logic and Foundations

Description

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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