9783540693185 - Proof Theory: The First Step into Impredicativity (Universitext) von Pohlers, Wolfram (3 Ergebnisse)

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Taschenbuch. Zustand: Neu. Proof Theory | The First Step into Impredicativity | Wolfram Pohlers | Taschenbuch | xiv | Englisch | 2008 | Springer | EAN 9783540693185 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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).