Zermelo-Fraenkel set theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Columbus, Ohio
Merrill
1968
|
| Series: | Merrill mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 164 S. |
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| 245 | 1 | 0 | |a Zermelo-Fraenkel set theory |c Seymour Hayden ; John F. Kennison |
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Record in the Search Index
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| adam_text | Table of Contents
Chapter 1
Groundrules 1
1 1 Introduction 1
1 2 Informal Logic 2
1 3 Zermelo Fraenkel Assumptions for the
Construction of Sets 10
1 4 Basic Consequences of the Assumptions 14
1 5 Ordered Pairs 17
Chapter 2
Relations and Functions 18
2 1 Functions 18
2 2 Relations 19
2 3 Equivalence Relations 21
2 4 Partial Ordering 24
2 5 Upper and Lower Bounds 25
2 6 Linear and Well Ordering 26
2 7 Properties of Mappings 27
2 8 Index Sets 29
Chapter 3
Binary Operations 31
3 1 Definitions 31
3 2 Classification of Binary Operations 32
3 3 Semigroups 35
3 4 Subsemigroups, Groups, Subgroups 38
3 5 The Permutations of a Set 42
3 6 Rings, Integral Domains, Fields 43
3 7 Isomorphisms and Homomorphisms 46
ix
x Zennelo Fraenkel Set Theory
Chapter 4
Ordinals, Cardinals, and the Axiom of Choice 50
4 1 Statement of the Axiom of Choice 50
4 2 Equivalent Forms of the Axiom of Choice 52
4 3 Ordinal Numbers 57
4 4 Cardinal Numbers 60
Chapter 5
The Axiom of Infinity and the Natural Numbers 66
5 1 Finite and Infinite Sets 66
5 2 Definition of the Set N 68
5 2a Peano s Postulates—an Alternative
Approach to the Natural Numbers 71
5 3 Inductive Definitions 73
5 4 Decimal Notation for Natural Numbers 79
Chapter 6
The Integers and the Rational Numbers 82
6 1 Introduction 82
6 2 An Intuitive View of the Integers 83
6 3 The Set Z of Integers 85
6 4 Ordered Integral Domains 88
6 5 Well Ordered Integral Domains 90
6 6 The Fundamental Theorem of Arithmetic 91
6 7 The Division Algorithm for Integers 93
6 8 The Set Q of Rational Numbers 94
Chapter 7
The Real and Complex Numbers 98
7 1 An Intuitive View of the Real Numbers 98
7 2 The Construction of R 100
7 3 Dedekind Complete Ordered Fields 102
7 4 Rational Exponents 105
Table of Contents xi
7 5 Cauchy Sequences in Ordered Fields 107
7 6 Cauchy Completions of Ordered Fields 113
7 7 Real Exponents 116
7 8 Notation for Real Numbers 117
7 9 Nested Sequences 120
7 10 Topology of the Real Line 122
7 11 The Complex Numbers 124
Chapter 8
Transflnite Arithmetic 128
8 1 Countable Sets 128
8 2 Products of Arbitrarily Many Sets 130
8 3 Infinite Sums and Products of Cardinals 133
8 4 Ordinal Addition, Subtraction, and
Multiplication 135
8 5 Transfinite Induction 138
8 6 Sums and Products of Infinitely Many
Ordinals 142
8 7 Notation for Infinite Cardinals and Ordinals 145
Appendix
Other Axioms and Approaches for Set Theory 149
A l Rank and Regularity 149
A 2 Godel Bernays Set Theory 153
A 3 Tarski Grothendieck Universes 157
References 159
Index 161
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:56:04Z |
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| language | English |
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| physical | XI, 164 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Merrill |
| record_format | marc |
| series2 | Merrill mathematics series |
| spelling | Hayden, Seymour Verfasser aut Zermelo-Fraenkel set theory Seymour Hayden ; John F. Kennison Columbus, Ohio Merrill 1968 XI, 164 S. txt rdacontent n rdamedia nc rdacarrier Merrill mathematics series Ensembles, Théorie des Set theory Theorie (DE-588)4059787-8 gnd rswk-swf Zermelo-Fraenkel-Axiome (DE-588)4190747-4 gnd rswk-swf Zermelo-Fraenkel-Axiome (DE-588)4190747-4 s Theorie (DE-588)4059787-8 s DE-604 Kennison, John F. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004541760&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hayden, Seymour Kennison, John F. Zermelo-Fraenkel set theory Ensembles, Théorie des Set theory Theorie (DE-588)4059787-8 gnd Zermelo-Fraenkel-Axiome (DE-588)4190747-4 gnd |
| subject_GND | (DE-588)4059787-8 (DE-588)4190747-4 |
| title | Zermelo-Fraenkel set theory |
| title_auth | Zermelo-Fraenkel set theory |
| title_exact_search | Zermelo-Fraenkel set theory |
| title_full | Zermelo-Fraenkel set theory Seymour Hayden ; John F. Kennison |
| title_fullStr | Zermelo-Fraenkel set theory Seymour Hayden ; John F. Kennison |
| title_full_unstemmed | Zermelo-Fraenkel set theory Seymour Hayden ; John F. Kennison |
| title_short | Zermelo-Fraenkel set theory |
| title_sort | zermelo fraenkel set theory |
| topic | Ensembles, Théorie des Set theory Theorie (DE-588)4059787-8 gnd Zermelo-Fraenkel-Axiome (DE-588)4190747-4 gnd |
| topic_facet | Ensembles, Théorie des Set theory Theorie Zermelo-Fraenkel-Axiome |
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