Axiomatic set theory
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1968
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Studies on logic and the foundations of mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 100 | 1 | |a Bernays, Paul |d 1888-1977 |e Verfasser |0 (DE-588)11865845X |4 aut | |
| 245 | 1 | 0 | |a Axiomatic set theory |c Paul Bernays. With a historical introduction by Abraham A. Fraenkel |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Amsterdam |b North-Holland |c 1968 | |
| 300 | |a VIII, 227 S. | ||
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| 490 | 0 | |a Studies on logic and the foundations of mathematics | |
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| 650 | 4 | |a Axiomatic set theory | |
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| adam_text | CONTENTS
Preface v
PART I. HISTORICAL INTRODUCTION
1. Introductory Remarks 3
2. Zermelo s Si stem. Equality and Extensionality 5
3. Constructive Axioms or General Set Theory 9
4. The Axiom op Choice 15
5. Axioms or Infinity and of Restriction 21
6. Development of Skt Theory from the Axioms of Z .... 26
7. Remarks on the Axiom Systems of von Neumann, Bernays,
Godel 31
PART II. AXIOMATIC SET THEORY
Introduction 39
Chapter I. The Frame of Looic and Class Theory 45
1. Predicate Calculus; Class Terms and Descriptions; Explicit
Definitions 45
2. Equality and Extensionality. Application to Descriptions . 52
3. Class Formalism. Class Operations 56
4. Functionality and Mappings 61
Chapter II. The Start of General Set Theory 65
1. The Axioms of General Set Theory 65
2. Aussonderungstheorem. Intersection 69
3. Sum Theorem. Theorem of Replacement 72
4. Functional Sets. One to one Correspondences 76
Chapter III. Ordinals; Natural Numbers; Finite Sets ... 80
1. Fundaments of the Theory of Ordinals 80
2. Existential Statements on Ordinals. Limit Numbers .... 86
3. Fundaments of Number Theory 89
4. Iteration. Primitive Recursion 92
5. Finite Sets and Classes 97
Chapter IV. Transfinite Recursion 100
1. The General Recursion Theorem 100
2. The Schema of Transfinite Recursion 104
3. Generated Numeration 109
vm CONTENTS
Chapter V. Power; Ordeb; Wellorder 114
1. Comparison of Powers 114
2. Order and Partial Order 118
3. Wellorder 124
Chapter VI. The Completing Axioms 130
1. The Potency Axiom 130
2. The Axiom of Choice 133
3. The Numeration Theorem. First Concepts of Cardinal Arith¬
metic 138
4. Zorn s Lemma and Related Principles 142
5. Axiom of Infinity. Denumerability 147
Chapter VII. Analysis; Cardinal Arithmetic; Abstract
Theories 155
1. Theory of Real Numbers 155
2. Some Topics of Ordinal Arithmetic 164
3. Cardinal Operations 173
4. Formal Laws on Cardinals 179
5. Abstract Theories 188
Chapter VIII. Further Strengthening of the Axiom System 195
1. A Strengthening of the Axiom of Choice 195
2. The Fundierungsaxiom 200
3. A one to one Correspondence between the Class of Ordinals
and the Class of all Sets 203
Index of Authors (Part I) 211
Index of Symbols (Part II) 213
Predicates 213
Functors and Operators 214
Primitive Symbols 215
Index of matters (Part II) 216
List of axioms (Part II) 218
Bibliography (Part I and II) 219
|
| any_adam_object | 1 |
| author | Bernays, Paul 1888-1977 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 QH 120 SK 130 SK 150 SK 155 |
| ctrlnum | (OCoLC)96775 (DE-599)BVBBV002280556 |
| dewey-full | 512/.817 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.817 |
| dewey-search | 512/.817 |
| dewey-sort | 3512 3817 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002280556 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001498582 |
| oclc_num | 96775 |
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| physical | VIII, 227 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | North-Holland |
| record_format | marc |
| series2 | Studies on logic and the foundations of mathematics |
| spellingShingle | Bernays, Paul 1888-1977 Axiomatic set theory Ensembles, Théorie des Axiomatic set theory Mengenlehre (DE-588)4074715-3 gnd Axiomatik (DE-588)4004038-0 gnd Axiomatische Mengenlehre (DE-588)4143743-3 gnd |
| subject_GND | (DE-588)4074715-3 (DE-588)4004038-0 (DE-588)4143743-3 |
| title | Axiomatic set theory |
| title_auth | Axiomatic set theory |
| title_exact_search | Axiomatic set theory |
| title_full | Axiomatic set theory Paul Bernays. With a historical introduction by Abraham A. Fraenkel |
| title_fullStr | Axiomatic set theory Paul Bernays. With a historical introduction by Abraham A. Fraenkel |
| title_full_unstemmed | Axiomatic set theory Paul Bernays. With a historical introduction by Abraham A. Fraenkel |
| title_short | Axiomatic set theory |
| title_sort | axiomatic set theory |
| topic | Ensembles, Théorie des Axiomatic set theory Mengenlehre (DE-588)4074715-3 gnd Axiomatik (DE-588)4004038-0 gnd Axiomatische Mengenlehre (DE-588)4143743-3 gnd |
| topic_facet | Ensembles, Théorie des Axiomatic set theory Mengenlehre Axiomatik Axiomatische Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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