Proof Theory

K. Schütte (Autor)

Buch | Softcover

XII, 302 Seiten

2011 | 1. Softcover reprint of the original 1st ed. 1977
Springer Berlin (Verlag)
978-3-642-66475-5 (ISBN)

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This book was originally intended to be the second edition of the book "Beweis theorie" (Grundlehren der mathematischen Wissenschaften, Band 103, Springer 1960), but in fact has been completely rewritten. As well as classical predicate logic we also treat intuitionistic predicate logic. The sentential calculus properties of classical formal and semiformal systems are treated using positive and negative parts of formulas as in the book "Beweistheorie". In a similar way we use right and left parts of formulas for intuitionistic predicate logic. We introduce the theory of functionals of finite types in order to present the Gi:idel interpretation of pure number theory. Instead of ramified type theory, type-free logic and the associated formalization of parts of analysis which we treated in the book "Beweistheorie", we have developed simple classical type theory and predicative analysis in a systematic way. Finally we have given consistency proofs for systems of lI~-analysis following the work of G. Takeuti. In order to do this we have introduced a constni'ctive system of notation for ordinals which goes far beyond the notation system in "Beweistheorie".

A. Pure Logic.- I. Fundamentals.- II. Classical Predicate Calculus.- III. Intuitionistic Predicate Calculus.- IV. Classical Simple Type Theory.- B. Systems of Arithmetic.- V. Ordinal Numbers and Ordinal Terms.- VI. Functional of Finite Type.- VII. Pure Number Theory.- C. Subsystems of Analysis.- VIII. Predicative Analysis.- IX. Higher Ordinals and Systems of ?11-Analysis.

Erscheint lt. Verlag	17.11.2011
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Übersetzer	J.N. Crossley
Zusatzinfo	XII, 302 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	554 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Beweistheorie • Calculus • Finite • Function • ordinal • Predicate logic • Proof • Proof theory • Type Theory
ISBN-10	3-642-66475-X / 364266475X
ISBN-13	978-3-642-66475-5 / 9783642664755
Zustand	Neuware