Set theory for the mathematician:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Francisco [u.a.]
Holden-Day
1967
|
| Schriftenreihe: | Holden-Day series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 387 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804121313736916992 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1. Introduction 1
1.1 Historical background 1
1.2 Mathematical logic 6
1.3 Axiomatic systems 20
Chapter 2. Class Algebra 23
2.1 Atoms, classes, sets, and the £ relation 23
2.2 The axiom of extensionality 24
2.3 Subclasses 25
2.4 Models 26
2.5 Classes 31
2.6 Class algebra 33
2.1 A decision procedure for class algebra 38
2.8 Sets 41
2.9 Summary of the axioms 44
Chapter 3. Functions and Relations 45
3.1 Unordered pairs, ordered pairs, and direct products 45
3.2 Relations 51
3.3 Functions 61
3.4 Equipollence 67
3.5 Infinite operations 69
3.6 The axioms of choice and regularity 77
3.7 Summary of the axioms 82
Chapter 4. Natural Numbers 84
4.1 Natural numbers 84
4.2 Mathematical induction 89
4.3 The recursion theorem 91
4.4 Addition and multiplication 96
4.5 The Schroder Bernstein Theorem 102
ix
x Contents
Chapter 5. Finite and Infinite Classes 106
5.1 Finite classes 106
5.2 Denumerable classes 107
*5.3 The principle of dependent choices 115
*5.4 The axiom of regularity again 117
*Chapter 6. The Rational and Real Numbers 120
6.1 Introduction 120
6.2 The integers 121
6.3 The rational numbers 126
6.4 Cauchy sequences of rational numbers 131
6.5 The real numbers 142
6.6 Decimal representation 151
Chapter 7. Ordering Relations 155
7.1 Partial ordering relations 155
7.2 Linear and well ordering relations 158
7.3 Transfinite induction 161
7.4 Isomorphisms 163
*7.5 Dense and continuous classes 166
Chapter 8. Ordinal Numbers 175
8.1 Introduction 175
8.2 Ordinals 176
8.3 Transfinite recursion theorem 184
*8.4 Addition and subtraction 188
*8.5 Multiplication and exponentiation 197
*8.6 Rank 211
* Chapter 9. Ordinal Number Theory 219
9.1 Normal form 219
9.2 Primes 229
9.3 Sequences and limits 234
9.4 Continuous functions 237
9.5 Epsilon numbers 242
Chapter 10. Propositions Equivalent to the Axiom of Choice 247
10.1 The well ordering theorem 247
10.2 The trichotomy 251
Contents xi
10.3 Maximal principles 253
*10.4 Applications 257
Chapter 11. Cardinal Numbers 265
11.1 Introduction 265
11.2 Definition 266
11.3 Alternative definition using the axiom of choice 268
*11.4 Alternative definition using the axiom of regularity 270
11.5 Initial ordinals and alephs 271
11.6 Cardinal arithmetic 273
*Chapter 12. Cardinal Numbers and the Axiom of Choice 280
12.1 Additional properties of cardinal numbers 280
12.2 Cardinal numbers and the axiom of choice 295
12.3 Infinite sums and products 310
^Chapter 13. The Generalized Continuum Hypothesis 317
13.1 Introduction 317
13.2 The generalized continuum hypothesis and the axiom of
choice 318
13.3 The aleph hypothesis 319
13.4 Cofinality 320
13.5 The generalized continuum hypothesis and cardinal num¬
bers 327
13.6 The continuum hypothesis 336
* Chapter 14. Additional Axioms 348
14.1 Inaccessible cardinals 348
14.2 The axiom of constructibility 353
Bibliography 373
Index of Symbols 379
Index of Terms 383
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:56:00Z |
| institution | BVB |
| language | English |
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| physical | XI, 387 S. |
| publishDate | 1967 |
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| publisher | Holden-Day |
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| series2 | Holden-Day series in mathematics |
| spelling | Rubin, Jean E. Verfasser aut Set theory for the mathematician Jean E. Rubin San Francisco [u.a.] Holden-Day 1967 XI, 387 S. txt rdacontent n rdamedia nc rdacarrier Holden-Day series in mathematics Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004539103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rubin, Jean E. Set theory for the mathematician Set theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Set theory for the mathematician |
| title_auth | Set theory for the mathematician |
| title_exact_search | Set theory for the mathematician |
| title_full | Set theory for the mathematician Jean E. Rubin |
| title_fullStr | Set theory for the mathematician Jean E. Rubin |
| title_full_unstemmed | Set theory for the mathematician Jean E. Rubin |
| title_short | Set theory for the mathematician |
| title_sort | set theory for the mathematician |
| topic | Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Set theory Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004539103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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