Wolfram Pohlers: Proof Theory | Taschenbuch

Cover: 9783540693185 | Proof Theory | The First Step into Impredicativity | Wolfram Pohlers

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Beschreibung

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).

Inhaltsverzeichnis

Historical Background.- Primitive Recursive Functions and Relations.- Ordinals.- Pure Logic.- Truth Complexity for ?11-Sentences.- Inductive Definitions.- The Ordinal Analysis for PA.- Autonomous Ordinals and the Limits of Predicativity.- Ordinal Analysis of the Theory for Inductive Definitions.- Provably Recursive Functions of NT.- Ordinal Analysis for Kripke-Platek Set Theory with Infinity.- Predicativity Revisited.- Nonmonotone Inductive Definitions.- Epilogue.

Erscheinungsjahr:	2008
Fachbereich:	Grundlagen
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 374 S. 5 s/w Illustr. 374 p. 5 illus.
ISBN-13:	9783540693185
ISBN-10:	3540693181
Sprache:	Englisch
Herstellernummer:	978-3-540-69318-5
Autor:	Pohlers, Wolfram
Auflage:	1st ed. 1989. 2nd printing 2008
Hersteller:	Springer Springer, Berlin Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Abbildungen:	XIV, 374 p. 5 illus.
Maße:	22 x 173 x 234 mm
Von/Mit:	Wolfram Pohlers
Erscheinungsdatum:	13.10.2008
Gewicht:	0,584 kg

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