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Gentzen's Centenary The Quest for Consistency /

Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re...

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Corporate Author: SpringerLink (Online service)
Other Authors: Kahle, Reinhard. (Editor, http://id.loc.gov/vocabulary/relators/edt), Rathjen, Michael. (Editor, http://id.loc.gov/vocabulary/relators/edt)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Subjects:
Mathematical logic.
Mathematical Logic and Foundations.
Mathematical Logic and Formal Languages.
Online Access:https://doi.org/10.1007/978-3-319-10103-3
Table of Contents:
  • Part I Reflections
  • Gentzen’s Consistency Proof in Context, Reinhard Kahle
  • Gentzen’s Anti-Formalist Views, Michael Detlefsen
  • The Use of Trustworthy Principles in a Revised Hilbert’s Program, Anton Setzer
  • Part II Gentzen’s Consistency Proofs
  • On Gentzen’s First Consistency Proof for Arithmetic, Wilfried Buchholz
  • From Hauptsatz to Hilfssatz, Jan von Plato
  • A Note on How to Extend Gentzen’s Second Consistency Proof to a Proof of Normalization for First Order Arithmetic, Dag Prawitz
  • A Direct Gentzen-Style Consistency Proof for Heyting Arithmetic, Annika Siders
  • Gentzen’s Original Consistency Proof and the Bar Theorem, W.W. Tait
  • Goodstein’s Theorem Revisited, Michael Rathjen
  • Part III Results
  • Cut Elimination In Situ, Sam Buss
  • Spector’s Proof of the Consistency of Analysis, Fernando Ferreira
  • Climbing Mount ε_0, Herman Ruge Jervell
  • Semi-Formal Calculi and Their Applications, Wolfram Pohlers
  • Part IV Developments
  • Proof Theory for Theories of Ordinals III: Π_N-Reflection, Toshiyasu Arai
  • A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions, Gerhard Jäger and Dieter Probst
  • Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games, Frederik Meskens and Andreas Weiermann
  • Non-deterministic Epsilon Substitution Method for PA and ID_1, Grigori Mints
  • A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis, Paulo Oliva and Thomas Powell
  • Well-Ordering Principles and Bar Induction, Michael Rathjen and Pedro Francisco Valencia Vizcaíno. .

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