Proof Theory - The First Step into Impredicativity (Paperback, 1st ed. 1989. 2nd printing 2008)

The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ] Wilhelms-Universitat ] in Munster ] . It was planned as a successor of Springer Lecture Notes in Mathematics 1407. H- ever, when preparing it, I decided to also include material which has not been treated in SLN 1407. Since the appearance of SLN 1407 many innovations in the area of - dinal analysis have taken place. Just to mention those of them which are addressed in this book: Buchholz simpli?ed local predicativity by the invention of operator controlled derivations (cf. Chapter 9, Chapter 11); Weiermann detected applications of methods of impredicative proof theory to the characterization of the provable recursive functions of predicative theories (cf. Chapter 10); Beckmann improved Gentzen's boundedness theorem (which appears as Stage Theorem (Theorem 6. 6. 1) in this book) to Theorem 6. 6. 9, a theorem which is very satisfying in itself - though its real importance lies in the ordinal analysis of systems, weaker than those treated here. Besides these innovations I also decided to include the analysis of the theory (? -REF) as an example of a subtheory of set theory whose ordinal analysis only 2 0 requires a ?rst step into impredicativity. The ordinal analysis of(? -FXP) of non- 0 1 0 monotone? -de?nable inductive de?nitions in Chapter 13 is an application of the 1 analysis of(? -REF)."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Universitext
Release date:	October 2008
First published:	2009
Authors:	Wolfram Pohlers
Dimensions:	235 x 155 x 21mm (L x W x T)
Format:	Paperback
Pages:	374
Edition:	1st ed. 1989. 2nd printing 2008
ISBN-13:	978-3-540-69318-5
Categories:	Books > Business & Economics > Business & management > Management & management techniques > Operational research Books > Science & Mathematics > Mathematics > Mathematical foundations > General
LSN:	3-540-69318-1
Barcode:	9783540693185

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