Book 2015

Gentzen's Centenary

The Quest for Consistency

Editors:

ISBN: 978-3-319-10102-6 (Print) 978-3-319-10103-3 (Online)

Table of contents (19 chapters)

  1. Front Matter

    Pages i-x

  2. Reflections

    1. Front Matter

      Pages 1-1

    2. No Access

      Chapter

      Pages 3-24

      Gentzen’s Consistency Proof in Context

    3. No Access

      Chapter

      Pages 25-44

      Gentzen’s Anti-Formalist Views

    4. No Access

      Chapter

      Pages 45-60

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

  3. Gentzen’s Consistency Proofs

    1. Front Matter

      Pages 61-61

    2. No Access

      Chapter

      Pages 63-87

      On Gentzen’s First Consistency Proof for Arithmetic

    3. No Access

      Chapter

      Pages 89-130

      From Hauptsatz to Hilfssatz

    4. No Access

      Chapter

      Pages 131-176

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

    5. No Access

      Chapter

      Pages 177-211

      A Direct Gentzen-Style Consistency Proof for Heyting Arithmetic

    6. No Access

      Chapter

      Pages 213-228

      Gentzen’s Original Consistency Proof and the Bar Theorem

    7. No Access

      Chapter

      Pages 229-242

      Goodstein’s Theorem Revisited

  4. Results

    1. Front Matter

      Pages 243-243

    2. No Access

      Chapter

      Pages 245-277

      Cut Elimination In Situ

    3. No Access

      Chapter

      Pages 279-300

      Spector’s Proof of the Consistency of Analysis

    4. No Access

      Chapter

      Pages 301-315

      Climbing Mount \(\varepsilon _{0}\)

    5. No Access

      Chapter

      Pages 317-354

      Semi-Formal Calculi and Their Applications

  5. Developments

    1. Front Matter

      Pages 355-355

    2. No Access

      Chapter

      Pages 357-424

      Proof Theory for Theories of Ordinals III: \(\Pi _{N}\) -Reflection

    3. No Access

      Chapter

      Pages 425-454

      A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

    4. No Access

      Chapter

      Pages 455-478

      Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games

    5. No Access

      Chapter

      Pages 479-500

      Non-deterministic Epsilon Substitution Method for PA and ID 1

    6. No Access

      Chapter

      Pages 501-531

      A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis

    7. No Access

      Chapter

      Pages 533-561

      Well-Ordering Principles and Bar Induction