| Where Is the Gödel-Point Hiding: Gentzen's Consistency Proof of 1936 and His Representation of Constructive Ordinals 2014 Edition Contributor(s): Horská, Anna (Author) |
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ISBN: 3319021702 ISBN-13: 9783319021706 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback Published: November 2013 |
| Additional Information |
| BISAC Categories: - Philosophy | Logic - Mathematics | Logic |
| Dewey: 160 |
| Series: Springerbriefs in Philosophy |
| Physical Information: 0.18" H x 6.14" W x 9.21" (0.30 lbs) 77 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |
