Set theory: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1995
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 167 S. graph. Darst. |
| ISBN: | 3764336978 0817636978 |
Staff View
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| 245 | 1 | 0 | |a Set theory |b an introduction |c Robert L. Vaught |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1995 | |
| 300 | |a X, 167 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | TABLE OF CONTENTS
Preface ix
Introduction 1
1. Sets and Relations and Operations among them 5
1. Set algebra and the set builder 6
2. Russell s paradox 11
3. Infinite unions and intersections 13
4. Ordered couples and Cartesian products 14
5. Relations and functions 16
6. Sets of sets, power set, arbitrary Cartesian product 20
7. Structures 23
8. Partial orders and orders 24
2. Cardinal Numbers and Finite Sets 29
1. Cardinal numbers, +, and 29
2. Natural numbers and finite sets 32
3. Multiplication and exponentiation 36
4. Definition by induction 38
5. Axiom of infinity, Peano axioms, Dedekind infinite sets 41
3. The Number Systems 45
1. Introductory remarks 45
2. Construction and characterization up to isomorphism
of the integers, rationals, and reals 46
4. More on Cardinal Numbers 49
1. The Cantor Bernstein Theorem 49
2. Infinite sums and products of cardinals 51
3. Different kinds of infinity 53
4. Ko, 2K°, and 22*0 the simplest infinite cardinals 55
5. Orders and Order Types 59
1. Ordered sums and products 59
2. Order types 60
6. Axiomatic Set Theory 65
1. A formalized language 65
2. The axioms of set theory 66
3. On Chapter 1 67
4. On Chapters 2 5 68
7. Well orderings, Cardinals, and Ordinals 71
1. Well orders 71
2. Von Neumann ordinals 75
3. The well ordering theorem 79
4. Defining A and TpA 81
5. Easy consequences for cardinals of the Well ordering
Principle 85
6. A harder consequence and its corollaries 85
7. The Continuum hypothesis 88
8. The Axiom of Regularity 91
1. Partial universes and the axiom of regularity 91
2. Consequences of regularity 94
3. Avoiding replacement 97
9. Logic and Formalized Theories 99
1. Language and grammar 100
2. Truth and tables 102
3. Formal proofs 103
4. Substitution for predicate symbols and relativization 107
5. Three forms of ZFC 110
10. Independence Proofs 113
1. Relativization of axioms to partial universes.
Consistency of adding Reg. 113
2. Three other consistency results 116
3. Informal note on the set theories NB and M 118
11. More on Cardinals and Ordinals 121
1. Character of cofinality 121
2. More on ordinal arithmetic 123
Appendix 129
Proofs of some results in Chapter 9 129
Bibliography 135
Other References 135
Recommendations for more advanced reading 136
Index 137
Solutions to Selected Problems
|
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| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 2. ed. |
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| isbn | 3764336978 0817636978 |
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| spelling | Vaught, Robert L. 1926-2002 Verfasser (DE-588)172431875 aut Set theory an introduction Robert L. Vaught 2. ed. Boston [u.a.] Birkhäuser 1995 X, 167 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ensembles, Théorie des Verzamelingen (wiskunde) gtt Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 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=006690782&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 |
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| title | Set theory an introduction |
| title_auth | Set theory an introduction |
| title_exact_search | Set theory an introduction |
| title_full | Set theory an introduction Robert L. Vaught |
| title_fullStr | Set theory an introduction Robert L. Vaught |
| title_full_unstemmed | Set theory an introduction Robert L. Vaught |
| title_short | Set theory |
| title_sort | set theory an introduction |
| title_sub | an introduction |
| topic | Ensembles, Théorie des Verzamelingen (wiskunde) gtt Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Ensembles, Théorie des Verzamelingen (wiskunde) Set theory Mengenlehre Einführung |
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