Gentzen's Centenary

- Toshiyasu Arai, Proof Theory for Theories of Ordinals III: \Pi_N-Reflection

- Wilfried Buchholz, On Gentzen's first consistency proof for arithmetic

- Sam Buss, Cut Elimination In Situ

- Michael Detlefsen, Gentzen's Anti-Formalist Views

- Fernando Ferreira, Spector's proof of the consistency of analysis

- Gerhard Jäger and Dieter Probst, A proof-theoretic analysis of theories for stratified inductive definitions

- Herman Jervell, Climbing Mount \epsilon_0

- Reinhard Kahle, Gentzen's Consistency Proof in Context

- Frederik Meskens and Andreas Weiermann Classifying phase transition thresholds for Goodstein sequences and Hydra games

- Grigori Mints, Non-Deterministic Epsilon Substitution Method for PA and ID_1

- Paulo Oliva and Thomas Powell, A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis

- Jan von Plato,  >From Hauptsatz to Hilfssatz

- Wolfram Pohlers, Semi-formal calculi and their applications

- Dag Prawitz, A note on Gentzen's 2nd consistency proof and normalization of natural deductions in 1st order arithmetic

- Michael Rathjen and Pedro Francisco Valencia Vizcaíno, Well ordering principles and Bar induction

- Anton Setzer, The Use of Trustworthy Principles in a Revised Hilbert's Program

- Annika Siders, A Direct Gentzen-style Consistency Proof for Heyting Arithmetic

- W. W. Tait, Gentzen's original consistency proof and the Bar Theorem

"The book collects for the first time individual studies which focus solely on this aspect of Gentzen's work. Because they admirably elucidate the historical, philosophical, and technical facets of his foundational papers in ordinal proof theory, the book can be recommended to everyone interested in these topics." (David Binder, Journal for General Philosophy of Science, Vol. 49, 2018)




"The volume is undoubtedly of a high-level technical content and thus of great interest for computer scientists and mathematical logicians. However, thanks to the numerous chapters containing philosophical reflections and historical information, the volume is also appealing for philosophers of logic." (Francesca Poggiolesi, History and Philosophy of Logic, Vol. 38 (3), March, 2017)

"The articles in this collection clearly offer a wide and lively description of Gentzen's work and of Gentzen's legacy. ... This volume will be for years to come an important key tool not only for people working in reductive and ordinal proof theory, but also for anyone more in general interested in the field of proof theory." (Enrico Moriconi, History and Philosophy of Logic, Vol. 38 (2), January, 2017)

"Gentzen's work has provided the blueprint, in many ways, for work in proof theory that has been extending its reach beyond arithmetic to subsystems of analysis and also to parts of set theory. ... This is an exciting volume: informative in many different ways about the background and current state of proof theory, in particular of those parts that have been shaped by Gentzen's work." (Wilfried Sieg, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 119, 2017)"This book is thefollow-on to the 2009 symposium in Leeds celebrating the centenary of the great German logician Gerhard Gentzen. It contains survey as well as technical chapters by highly respected proof theorists. It is of interest to logicians and computer scientists working in