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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). Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
13.10.2008
Sprache
Englisch
EAN
9783540693185
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Universitext
Sonderedition
Nein
Autor
Wolfram Pohlers
Seitenanzahl
374
Einbandart
Taschenbuch
Buch Untertitel
The First Step into Impredicativity
Schlagwörter
Arithmetic, Derivation, Finite, Proof theory, calculus, function, impredicativity, ordinal, ordinal analysis, proof, recursion, set theory, sub-systems of second order number theory and set theory, theorem, well-ordering principle
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
KJT - Unternehmensforschung
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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