Proof Theory: The First Step Into Impredicativity

By Wolfram Pohlers

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).

• Format: Paperback
• Language: English
• ISBN: 3540693181
• ISBN13: 9783540693185
• Release Date: October 2008
• Publisher: Springer
• Length: 374 Pages
• Weight: 1.65 lbs.
• Dimensions: 0.9" x 6.1" x 9.1"