Gentzen's centenary : the quest for consistency /: the quest for consistency. ([2015])

• Record Type: Book
• Further Information: Note: Reinhard Kahle, Michael Rathjen, editors.
• Editors: Kahle, Reinhard, 1967-; Rathjen, Michael
• Contents: Preface -- In Memoriam: Grigori Mints -- Part I: Reflections -- 1. Reinhard Kahle: Gentzen's Consistency Proof in Context -- 2. Michael Detlefsen: Gentzen's Anti-Formalist Views -- 3. Anton Setzer: The Use of Trustworthy Principles in a Revised Hilbert's Program -- Part II: Gentzen's Consistency Proof -- 4. Wilfried Buchholz: On Gentzen's first consistency proof for arithmetic -- 5. Jan von Plato: From \emph{Hauptsatz} to \emph{Hilfssatz} (with an appendix by Siders/von Plato) -- 6. Dag Prawitz: Extending Gentzen's 2nd consistency proof to normalization of natural deductions in 1st order arithmetic -- 7. Annika Siders: A Direct Gentzen-style Consistency Proof for Heyting Arithmetic -- 8. W.W. Tait: Gentzen's original consistency proof and the Bar Theorem -- Part III: Results -- 9. Sam Buss: Cut Elimination \emph{In Situ} -- 10. Fernando Ferreira: Spector's proof of the consistency of analysis -- 11. Herman Jervell: Climbing Mount $\varepsilon_0$ -- 12. Wolfram Pohlers: Semi-formal calculi and their applications -- Part IV: Developments -- 13. Toshiyasu Arai: Proof Theory for Theories of Ordinals III: $\Pi_{N}$-Reflection -- 14. Gerhard Jäger and Dieter Probst: A proof-theoretic analysis of theories for stratified inductive definitions -- 15. Frederik Meskens and Andreas Weiermann: Classifying phase transition thresholds for Goodstein sequences and Hydra games -- 16. Grigori Mints: Non-Deterministic Epsilon Substitution Method for $\mathsf{PA}$ and $\mathsf{ID}_1$ -- 17. Paulo Oliva and Thomas Powell: A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis -- 18. Michael Rathjen and Pedro Francisco Valencia Vizcaíno: Well ordering principles and Bar induction.
• Publisher Details: Cham : Springer
• Publication Date: 2015
• Extent: 1 online resource (x, 561 pages)
• Subjects: 511.3; Mathematics; Proof theory; MATHEMATICS -- General; Proof theory; Mathematics -- Logic; Mathematical theory of computation; Logic, Symbolic and mathematical; Computer science; Mathematical foundations; Electronic books
• Languages: English
• ISBNs: 9783319101033
• Related ISBNs: 331910103X; 9783319101026; 3319101021
• Notes: Note: Includes bibliographical references.; Note: Vendor-supplied metadata.
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• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.