Gentzen's Centenary

Chapter 1 Gentzen’s Consistency Proof in Context

Chapter 2 Gentzen’s Anti-Formalist Views

Chapter 3 The Use of Trustworthy Principles in a Revised Hilbert’s Program

Chapter 4 On Gentzen’s First Consistency Proof for Arithmetic

Chapter 5 From Hauptsatz to Hilfssatz

Chapter 6 A Note on How to Extend Gentzen’s Second Consistency Proof to a Proof of Normalization for First Order Arithmetic

Chapter 7 A Direct Gentzen-Style Consistency Proof for Heyting Arithmetic

Chapter 8 Gentzen’s Original Consistency Proof and the Bar Theorem

Chapter 9 Goodstein’s Theorem Revisited

Chapter 10 Cut Elimination In Situ

Chapter 11 Spector’s Proof of the Consistency of Analysis

Chapter 12 Climbing Mount $$\varepsilon _{0}$$

Chapter 13 Semi-Formal Calculi and Their Applications

Chapter 14 Proof Theory for Theories of Ordinals III: $$\Pi _{N}$$ -Reflection

Chapter 15 A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

Chapter 16 Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games

Chapter 17 Non-deterministic Epsilon Substitution Method for PA and ID 1

Chapter 18 A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis