Saved from the Cellar : Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics. 1st ed. 2017

種類:

電子ブック

責任表示:

by Jan von Plato

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• von Plato, Jan.
• SpringerLink (Online service)

シリーズ名:

Sources and Studies in the History of Mathematics and Physical Sciences ;

ISBN:

9783319421209 [3319421204]    

注記:

Part I: A Sketch of Gentzen's Life and Work -- 1. Overture -- 2. Gentzen's years of study -- Dr. Gentzen's arduous years in Nazi Germany -- 4. The scientific accomplishments -- 5. Loose ends -- 6. Gentzen's genuis -- Part II: Overview of the Shorthand Notes -- 1. Gentzen's series of stenographic manuscripts -- 2. The items in this collection -- Practical remarks on the manuscripts -- Manuscript illustrations -- The German alphabet in Latin, Sutterlin, and Fraktur Type -- Bibliography for parts I and II -- Index of names for Parts I and II -- Part III: The Original Writings -- 1. Reduction of number-theoretic problems to predicate logic -- 2. Replacement of functions by predicates -- 3. The formation of abstract concepts -- 4. Five different forms of natural calculi -- 5. Formal conception of correctness in arithmetic I -- 6. Investigations into logical inferences -- 7. Reduction of classical to intuitionistic logic -- 8. CV of the candidate Gerhard Gentzen.-0 9. Letters to Heyting -- 10. Formal conception of
Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Gödel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations o

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