Proof Theory (Grundlehren der mathematischen Wissenschaften)

US: Springer, 1977. Ex-Lib. Hardcover. Very Good-/None. Grundlehren der mathematischen Wissenschaften Series Yellow cloth boards, toned and lightly soiled from fingerprints. Page edges stamped by university library. End papers similarly stamped. Text is unmarked. Rear pastedown has adhesive residue, and rear ffep has scar where pocket removed. Binding is sound. 8vo. BOOK INFO: See photos for Table of Contents. This book was originally intended to be the second edition of the book Beweistheorie (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 Godel 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 constructive system of notation for ordinals which goes far beyond the notation system in Beweistheorie. (~from the Preface by Schutte). Includes bibliography and subject index.