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Proof Theory:

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1. Verfasser:	Schütte, Kurt 1909-1998 (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Berlin, Heidelberg Springer Berlin Heidelberg 1977
Schriftenreihe:	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 225
Schlagworte:	Mathematics Mathematics, general Mathematik Beweistheorie
Online-Zugang:	Volltext
Beschreibung:	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 Gödel 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 II-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"
Beschreibung:	1 Online-Ressource (XII, 302 p)
ISBN:	9783642664731 9783642664755
DOI:	10.1007/978-3-642-66473-1

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Datensatz im Suchindex

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isbn	9783642664731 9783642664755
language	English
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series	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
series2	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
spelling	Schütte, Kurt 1909-1998 Verfasser (DE-588)118611127 aut Proof Theory by Kurt Schütte Berlin, Heidelberg Springer Berlin Heidelberg 1977 1 Online-Ressource (XII, 302 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 225 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 Gödel 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 II-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 Mathematics, general Mathematik Beweistheorie (DE-588)4145177-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Beweistheorie (DE-588)4145177-6 s 1\p DE-604 Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 225 (DE-604)BV049758308 225 https://doi.org/10.1007/978-3-642-66473-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Schütte, Kurt 1909-1998 Proof Theory Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Mathematics Mathematics, general Mathematik Beweistheorie (DE-588)4145177-6 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4145177-6 (DE-588)4037944-9
title	Proof Theory
title_auth	Proof Theory
title_exact_search	Proof Theory
title_full	Proof Theory by Kurt Schütte
title_fullStr	Proof Theory by Kurt Schütte
title_full_unstemmed	Proof Theory by Kurt Schütte
title_short	Proof Theory
title_sort	proof theory
topic	Mathematics Mathematics, general Mathematik Beweistheorie (DE-588)4145177-6 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Mathematics Mathematics, general Mathematik Beweistheorie
url	https://doi.org/10.1007/978-3-642-66473-1
volume_link	(DE-604)BV049758308
work_keys_str_mv	AT schuttekurt prooftheory

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