عنوان

Proof Theory

(Number (ISBN

3642664733

(Number (ISBN

364266475X

(Number (ISBN

9783642664731

(Number (ISBN

9783642664755

Number

b572333

Title Proper

Proof Theory

General Material Designation

[Book]

First Statement of Responsibility

by Kurt Schütte.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1977

Series Title

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 225.

Text of Note

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.

Text of Note

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."

Mathematics.

by Kurt Schütte.

K Schütte

Electronic name

[Book]

Y