Proof Theory (Grundlehren der mathematischen Wissenschaften)

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9783642664755: Proof Theory (Grundlehren der mathematischen Wissenschaften)
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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".

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9783540079118: Proof Theory (Grundlehren der mathematischen Wissenschaften)

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ISBN 10:  3540079114 ISBN 13:  9783540079118
Publisher: Springer, 1977
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Book Description Springer. Paperback. Condition: New. 320 pages. Dimensions: 9.6in. x 6.7in. x 0.7in.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 constnictive system of notation for ordinals which goes far beyond the notation system in Beweistheorie. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9783642664755

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Book Description Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 2011. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.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 . Softcover reprint of the original 1st ed. 1977. Seller Inventory # AAV9783642664755

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