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Where is the Godel-Point Hiding: Gentzen's Consistency Proof of 1936 and His Representation of Constructive Ordinals
Anna Horska
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Description for Where is the Godel-Point Hiding: Gentzen's Consistency Proof of 1936 and His Representation of Constructive Ordinals
Paperback. Series: SpringerBriefs in Philosophy. Num Pages: 77 pages, biography. BIC Classification: HPL; PBC. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 4. Weight in Grams: 150.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2013
Publisher
Springer International Publishing AG Switzerland
Number of pages
77
Condition
New
Series
SpringerBriefs in Philosophy
Number of Pages
77
Place of Publication
Cham, Switzerland
ISBN
9783319021706
SKU
V9783319021706
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
Reviews for Where is the Godel-Point Hiding: Gentzen's Consistency Proof of 1936 and His Representation of Constructive Ordinals
From the book reviews: “This book deals with G. Gentzen’s classical 1936 article on the consistency of arithmetic … . The result is a clear exposition of the full proof with all details and with the ideas behind the proof visible. … All in all, the author of this book has accomplished the difficult task of making Gentzen’s original ... Read more