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This book is a compilation of papers presented at the 2002 European
Summer Meeting of the Association for Symbolic Logic and the
associated Colloquium Logicum 2002 conference. It includes
tutorials and research articles from some of the world's preeminent
logicians. The topics presented span all areas of mathematical
logic, with a particular emphasis on Computability Theory and Proof
Theory.
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)."
Logic Colloquium '02 includes articles from some of the world's
preeminent logicians. The topics span all areas of mathematical
logic, but with an emphasis on Computability Theory and Proof
Theory. This book will be of interest to graduate students and
researchers in the field of mathematical logic.
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