Where is the Gödel-point hiding : Gentzen's consistency proof of 1936 and his representation of constructive ordinals /

Where is the Gödel-point hiding : Gentzen's consistency proof of 1936 and his representation of constructive ordinals /

Saved in:

Bibliographic Details
Author / Creator:	Horská, Anna, author.
Imprint:	Cham : Springer, 2014.
Description:	1 online resource (ix, 77 pages).
Language:	English
Series:	SpringerBriefs in Philosophy, 2211-4548 SpringerBriefs in philosophy,
Subject:	Proof theory. Numbers, Ordinal. Gödel numbers. Gödel numbers. Numbers, Ordinal. Proof theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11081871

Hidden Bibliographic Details
ISBN:	9783319021713 3319021710 9783319021706
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed October 28, 2013).
Summary:	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.
Standard no.:	10.1007/978-3-319-02171-3

Table of Contents:

Preliminaries
Ordinal numbers
Consistency proof.