The joy of sets: fundamentals of contemporary set theory
Gespeichert in:
| Vorheriger Titel: | Devlin, Keith J. Fundamentals of contemporary set theory |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1993
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 192 S. |
| ISBN: | 0387940944 3540940944 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface v
1 Naive Set Theory 1
1.1 What is a Set? 1
1.2 Operations on Sets 4
1.3 Notation for Sets 6
1.4 Sets of Sets 7
1.5 Relations 10
1.6 Functions 12
1.7 Well Orderings and Ordinals 16
1.8 Problems 25
2 The Zermelo—Fraenkel Axioms 29
2.1 The Language of Set Theory 30
2.2 The Cumulative Hierarchy of Sets 35
2.3 The Zermelo Fraenkel Axioms 40
2.4 Classes 46
2.5 Set Theory as an Axiomatic Theory 50
2.6 The Recursion Principle 51
2.7 The Axiom of Choice 56
2.8 Problems 63
3 Ordinal and Cardinal Numbers 66
3.1 Ordinal Numbers 66
3.2 Addition of Ordinals 68
3.3 Multiplication of Ordinals 69
3.4 Sequences of Ordinals 71
3.5 Ordinal Exponentiation 74
3.6 Cardinality, Cardinal Numbers 75
3.7 Arithmetic of Cardinal Numbers 82
3.8 Regular and Singular Cardinals 88
3.9 Cardinal Exponentiation 91
ix
x CONTENTS
3.10 Inaccessible Cardinals 95
3.11 Problems 98
4 Topics in Pure Set Theory 101
4.1 The Borel Hierarchy 101
4.2 Closed Unbounded Sets 103
4.3 Stationary Sets and Regressive Functions 106
4.4 Trees 109
4.5 Extensions of Lebesgue Measure 113
4.6 A Result About the GCH 116
5 The Axiom of Constructibility 120
5.1 Constructible Sets 120
5.2 The Constructible Hierarchy 123
5.3 The Axiom of Constructibility 124
5.4 The Consistency of V = L 127
5.5 Use of the Axiom of Constructibility 128
6 Independence Proofs in Set Theory 130
6.1 Some Undecidable Statements 130
6.2 The Idea of a Boolean Valued Universe 130
6.3 The Boolean Valued Universe 133
6.4 VB and V 136
6.5 Boolean Valued Sets and Independence Proofs 137
6.6 The Nonprovability of the CH 139
7 Non Well Founded Set Theory 143
7.1 Set Membership Diagrams 145
7.2 The Anti Foundation Axiom 151
7.3 The Solution Lemma 156
7.4 Inductive Definitions Under AFA 159
7.5 Graphs and Systems 163
7.6 Proof of the Solution Lemma 168
7.7 Co Inductive Definitions 169
7.8 A Model of ZF +AFA 173
Bibliography 185
Glossary of Symbols 185
Index 189
|
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 511.3/2220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 20 |
| dewey-search | 511.3/22 20 |
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| discipline | Mathematik Philosophie |
| edition | 2. ed. |
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| indexdate | 2024-07-09T17:26:26Z |
| institution | BVB |
| isbn | 0387940944 3540940944 |
| language | English |
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| physical | X, 192 S. |
| publishDate | 1993 |
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| series2 | Undergraduate texts in mathematics |
| spelling | Devlin, Keith J. 1947- Verfasser (DE-588)123265460 aut The joy of sets fundamentals of contemporary set theory Keith Devlin 2. ed. New York [u.a.] Springer 1993 X, 192 S. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Mengenlehre Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 Frühere Ausg. u.d.T. Devlin, Keith J. Fundamentals of contemporary set theory HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005869354&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Devlin, Keith J. 1947- The joy of sets fundamentals of contemporary set theory Mengenlehre Set theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | The joy of sets fundamentals of contemporary set theory |
| title_auth | The joy of sets fundamentals of contemporary set theory |
| title_exact_search | The joy of sets fundamentals of contemporary set theory |
| title_full | The joy of sets fundamentals of contemporary set theory Keith Devlin |
| title_fullStr | The joy of sets fundamentals of contemporary set theory Keith Devlin |
| title_full_unstemmed | The joy of sets fundamentals of contemporary set theory Keith Devlin |
| title_old | Devlin, Keith J. Fundamentals of contemporary set theory |
| title_short | The joy of sets |
| title_sort | the joy of sets fundamentals of contemporary set theory |
| title_sub | fundamentals of contemporary set theory |
| topic | Mengenlehre Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Mengenlehre Set theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005869354&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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