Saved from the Cellar Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics /

Saved from the Cellar Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics /

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,...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: von Plato, Jan (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
Σειρά:Sources and Studies in the History of Mathematics and Physical Sciences,
Θέματα:
Mathematics.
History.
Mathematical logic.
History of Mathematical Sciences.
Mathematical Logic and Foundations.
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • 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 correctness in arithmetic II
  • 11. Proof theory of number theory
  • 12. Consistency of artihmetic, for publication
  • 13. Correspondence with Paul Bernays
  • 14. Forms of type theory
  • 15. Predicate logic
  • 16. Propositional logic
  • 17. Foundational research in mathematics
  • Table of cross-references in the Gentzen papers
  • Index of names in the Gentzen papers
  • Index of subjects in the Gentzen papers.

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