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...
| Συγγραφή απο Οργανισμό/Αρχή: | |
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| Άλλοι συγγραφείς: | , |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Έκδοση: | 1st ed. 2015. |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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. .
