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Bibliographic Details
Main Author:	Takeuti, Gaisi 1926-2017 (Author)
Format:	Book
Language:	English
Published:	Amsterdam u.a. North-Holland 1987
Edition:	2. ed.
Series:	Studies in logic and the foundations of mathematics 81.
Subjects:	Mathematics - Proof Bewijstheorie Preuve, Théorie de la Mathematik Proof theory Mathematische Logik Beweistheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 490 S.
ISBN:	0444879439

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MARC


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adam_text	CONTENTS Preface v Preface to the second edition vii Contents ix Introduction 1 PART I. FIRST ORDER SYSTEMS 3 Chapter 1. First Order Predicate Calculus 5 § 1. Formalization of statements 5 §2. Formal proofs and related concepts 9 §3. A formulation of intuitionistic predicate calculus .... 18 §4. Axiom systems 20 §5. The cut elimination theorem 21 §6. Some consequences of the cut elimination theorem ... 28 §7. The predicate calculus with equality 37 §8. The completeness theorem 40 Chapter 2. Peano Arithmetic 75 §9. A formulation of Peano arithmetic 75 §10. The incompleteness theorem 79 §11. A discussion of ordinals from a finitist standpoint ... 86 §12. A consistency proof of PA 101 §13. Provable well orderings 147 §14. An additional topic 156 PART II. SECOND ORDER AND FINITE ORDER SYSTEMS 159 Chapter 3. Second Order Systems and Simple Type Theory 165 §15. Second order predicate calculus 165 §16. Some systems of second order predicate calculus .... 172 §17. The theory of relativization 177 §18. Truth definition for first order arithmetic 183 §19. The interpretation of a system of second order arithmetic . 188 §20. Simple type theory 192 §21. The cut elimination theorem for simple type theory . . . 197 Chapter 4. Infinitary Logic 208 §22. Infinitary logic with homogeneous quantifiers 211 X CONTENTS §23. Determinate logic 236 §24. A general theory of heterogeneous quantifiers 264 PART III. CONSISTENCY PROBLEMS 295 Chapter 5. Consistency Proofs 298 §25. Introduction 298 §26. Ordinal diagrams 303 §27. A consistency proof of second order arithmetic with the /Ji comprehension axiom 320 §28. A consistency proof for a system with inductive definitions 350 Chapter 6. Some Applications of Consistency Proofs . 361 §29. Provable well orderings 361 §30. The i7j comprehension axiom and the a rule 363 §31. Reflection principles 368 Postscript 381 APPENDIX 393 Proof Theory by Georg Kreisel 395 Contributions of the Schutte School by Wolfram Pohlers 406 Subsystems of 7^ and Reverse Mathematics by Stephen G. Simpson 432 Proof Theory: A Personal Report by Solomon Feferman . 447 Index 487
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physical	X, 490 S.
publishDate	1987
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series	Studies in logic and the foundations of mathematics
series2	Studies in logic and the foundations of mathematics
spelling	Takeuti, Gaisi 1926-2017 Verfasser (DE-588)107888580 aut Proof theory Gaisi Takeuti 2. ed. Amsterdam u.a. North-Holland 1987 X, 490 S. txt rdacontent n rdamedia nc rdacarrier Studies in logic and the foundations of mathematics 81. Mathematics - Proof Bewijstheorie gtt Preuve, Théorie de la Mathematik Proof theory Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Mathematik (DE-588)4037944-9 s Beweistheorie (DE-588)4145177-6 s 1\p DE-604 Studies in logic and the foundations of mathematics 81. (DE-604)BV000893472 81 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004171993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Takeuti, Gaisi 1926-2017 Proof theory Studies in logic and the foundations of mathematics Mathematics - Proof Bewijstheorie gtt Preuve, Théorie de la Mathematik Proof theory Mathematische Logik (DE-588)4037951-6 gnd Mathematik (DE-588)4037944-9 gnd Beweistheorie (DE-588)4145177-6 gnd
subject_GND	(DE-588)4037951-6 (DE-588)4037944-9 (DE-588)4145177-6
title	Proof theory
title_auth	Proof theory
title_exact_search	Proof theory
title_full	Proof theory Gaisi Takeuti
title_fullStr	Proof theory Gaisi Takeuti
title_full_unstemmed	Proof theory Gaisi Takeuti
title_short	Proof theory
title_sort	proof theory
topic	Mathematics - Proof Bewijstheorie gtt Preuve, Théorie de la Mathematik Proof theory Mathematische Logik (DE-588)4037951-6 gnd Mathematik (DE-588)4037944-9 gnd Beweistheorie (DE-588)4145177-6 gnd
topic_facet	Mathematics - Proof Bewijstheorie Preuve, Théorie de la Mathematik Proof theory Mathematische Logik Beweistheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004171993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT takeutigaisi prooftheory

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