Two applications of logic to mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
1978
|
| Schriftenreihe: | Kanô memorial lectures.
3. Nihon Sugakkai: Publications of the Mathematical Society of Japan. 13. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 137 S. |
| ISBN: | 069108212X |
Internformat
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| 245 | 1 | 0 | |a Two applications of logic to mathematics |c by Gaisi Takeuti |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1978 | |
| 300 | |a VIII, 137 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Kanô memorial lectures. |v 3. | |
| 490 | 1 | |a Nihon Sugakkai: Publications of the Mathematical Society of Japan. |v 13. | |
| 650 | 4 | |a logika | |
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Datensatz im Suchindex
| _version_ | 1804118041630343168 |
|---|---|
| adam_text | Contents
Preface
Introduction 1
Parti
Boolean Valued Analysis
Chapter 1 Boolean Valued Analysis Using Projection Algebras 6
§ 1. Hilbert space 6
§ 2. The model FW 7
§ 3. Real numbers in K J 15
§ 4. The interpretation of elementary theorems 21
§ 5. Miscellaneous interpretations 29
§ 6. Convergence 31
§ 7. Semi group of self adjoint operators 33
§ 8. Complete Boolean algebras of Banach spaces 38
§ 9. Piecewise convergence 40
§10. Simultaneous spectrums 42
§11. Quantum Logic 46
Chapter 2 Boolean Valued Analysis Using Measure Algebras 51
§ 1. Measure algebras 51
§ 2. Real numbers in the model 52
§ 3. Continuous functions in the model 56
§ 4. Baire functions and Borel sets in the model 60
§ 5. Integration and differentiation in the model 63
§ 6. Relation between projection algebras and
measure algebras 68
References 71
Part II
A Conservative Extension of Peano Arithmetic
Chapter 1 Real Analysis 77
§ 1. The first system 77
viii Contents
§ 2. The second system 89
§ 3. Defining reals 91
§ 4. Functions 93
§ 5. Sequences 96
§ 6. Continuous functions 98
§ 7. Differentiation 101
§ 8. Integration 104
§ 9. Sequences of functions 106
§ 10. Infinite series and series of functions 107
§ 11. Higher derivatives 110
§ 12. Functions of several variables 112
Chapter 2 Complex Analysis 114
§ 1. A system of complex numbers 114
§ 2. Analytic functions 119
§ 3. Integration 122
§ 4. Cauchy s Theorem for nice regions 125
§ 5. Cauchy s Integral Formula 127
§ 6. The general form of Cauchy s Theorem 132
§ 7. Miscellaneous remarks 133
§ 8. Final remarks 134
References 136
Index 139
|
| any_adam_object | 1 |
| author | Takeuti, Gaisi 1926-2017 |
| author_GND | (DE-588)107888580 |
| author_facet | Takeuti, Gaisi 1926-2017 |
| author_role | aut |
| author_sort | Takeuti, Gaisi 1926-2017 |
| author_variant | g t gt |
| building | Verbundindex |
| bvnumber | BV003696991 |
| classification_rvk | SK 130 SK 150 |
| ctrlnum | (OCoLC)438847531 (DE-599)BVBBV003696991 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003696991 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:00Z |
| institution | BVB |
| isbn | 069108212X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002353021 |
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| physical | VIII, 137 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Kanô memorial lectures. Nihon Sugakkai: Publications of the Mathematical Society of Japan. |
| series2 | Kanô memorial lectures. Nihon Sugakkai: Publications of the Mathematical Society of Japan. |
| spelling | Takeuti, Gaisi 1926-2017 Verfasser (DE-588)107888580 aut Two applications of logic to mathematics by Gaisi Takeuti Princeton, NJ Princeton Univ. Press 1978 VIII, 137 S. txt rdacontent n rdamedia nc rdacarrier Kanô memorial lectures. 3. Nihon Sugakkai: Publications of the Mathematical Society of Japan. 13. logika Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 s Analysis (DE-588)4001865-9 s DE-604 Mathematische Logik (DE-588)4037951-6 s Kanô memorial lectures. 3. (DE-604)BV002788448 3. Nihon Sugakkai: Publications of the Mathematical Society of Japan. 13. (DE-604)BV001888196 13. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002353021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Takeuti, Gaisi 1926-2017 Two applications of logic to mathematics Kanô memorial lectures. Nihon Sugakkai: Publications of the Mathematical Society of Japan. logika Mathematische Logik (DE-588)4037951-6 gnd Boolesche Algebra (DE-588)4146280-4 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4146280-4 (DE-588)4001865-9 |
| title | Two applications of logic to mathematics |
| title_auth | Two applications of logic to mathematics |
| title_exact_search | Two applications of logic to mathematics |
| title_full | Two applications of logic to mathematics by Gaisi Takeuti |
| title_fullStr | Two applications of logic to mathematics by Gaisi Takeuti |
| title_full_unstemmed | Two applications of logic to mathematics by Gaisi Takeuti |
| title_short | Two applications of logic to mathematics |
| title_sort | two applications of logic to mathematics |
| topic | logika Mathematische Logik (DE-588)4037951-6 gnd Boolesche Algebra (DE-588)4146280-4 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | logika Mathematische Logik Boolesche Algebra Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002353021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002788448 (DE-604)BV001888196 |
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