A theory of sets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Orlando u.a.
Acad. Press
1986
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
108 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXII, 179 S. |
| ISBN: | 0125079524 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804115003837513728 |
|---|---|
| adam_text | CONTENTS
Foreword xi
Preface xxix
0. Language and Inference 1
Introduction 1
Replacement 3
Expressions 4
Rudiments 5
Schematic Replacement 8
Orienting Definitions 9
Free Variables and Formulas 10
Indicial and Accepted Variables 14
Rules of Inference; Theorems 17
Initiation 17
Detachment 17
Substitution 17
Schematic Substitution 17
Indicial Substitution 17
Universalization 18
Theory of Notation 19
Demonstrations 32
Chains 34
1. Logic 39
Definitional Axioms for Logic 39
Axioms of Definition for Logic 40
Axioms for Logic 40
Supplementary Rules of Inference 58
vii
viii Contents
2. Set Theory 63
Preliminaries 63
Orienting Definitions 63
Logical Definitional Axioms for Set Theory 65
Set Theoretic Definitional Axioms for Set Theory 65
Axiom of Definition for Set Theory 65
Axioms for Set Theory 65
The Theorem of Extent 67
Some Aspects of Equality 72
Classification 74
The Theorem of Classification 76
The Role of Replacement 78
The Theorem of Replacement 79
The Theorem of Heredity 80
The Theorem of Subsets 80
The Theorem of Amalgamation 81
The Theorem of Unions 81
Singletons 82
Ordered Pairs 83
The Ordered Pair Theorems 88
Substitution 88
Unicity 91
The Theorem of Unicity 93
Relations 93
Functions 97
Ordinals 100
Definition by Induction 103
The General Induction Theorem 106
The Ordinary Induction Theorems 107
Regularity and Choice 107
The Theorems of Choice 113
Maximality 114
Maximal Principle 115
Hausdorff s Maximal Principle 118
The Inductive Principle of Inclusion 120
Well Ordering 121
The Well Ordering Theorems 123
Contents lx
Natural Numbers 124
Sequences 126
Reiteration 128
Fixed Sets and Bipartition 129
The Theorem of Bipartition 133
Equinumerosity 134
The Cantor Bernstein Theorem 135
Cardinals 138
Cardinality 139
The Theorems of Cardinality 141
Cantor s Power Theorem 144
Cardinal Arithmetic 144
Direct Extensions 146
Families of Sets 147
Tuples 150
A. The Construction of Definitions 153
The Structure of Basic Forms 154
The Structure of Definitions 156
Adherence and Translatability 159
B. The Consistency of the Axiom of Size 163
C. Axiomatic Equivalence 167
Index of Constants 169
General Index 173
|
| any_adam_object | 1 |
| author | Morse, Anthony P. |
| author_facet | Morse, Anthony P. |
| author_role | aut |
| author_sort | Morse, Anthony P. |
| author_variant | a p m ap apm |
| building | Verbundindex |
| bvnumber | BV000562041 |
| classification_rvk | SK 150 |
| ctrlnum | (OCoLC)241697067 (DE-599)BVBBV000562041 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV000562041 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:15:42Z |
| institution | BVB |
| isbn | 0125079524 |
| language | Undetermined |
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| physical | XXXII, 179 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Acad. Press |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Morse, Anthony P. Verfasser aut A theory of sets 2. ed. Orlando u.a. Acad. Press 1986 XXXII, 179 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 108 Logik (DE-588)4036202-4 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Axiomatische Mengenlehre (DE-588)4143743-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mengenlehre (DE-588)4074715-3 s Logik (DE-588)4036202-4 s DE-604 Axiomatische Mengenlehre (DE-588)4143743-3 s Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Pure and applied mathematics 108 (DE-604)BV010177228 108 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000346289&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 |
| spellingShingle | Morse, Anthony P. A theory of sets Pure and applied mathematics Logik (DE-588)4036202-4 gnd Mengenlehre (DE-588)4074715-3 gnd Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4074715-3 (DE-588)4143743-3 (DE-588)4037951-6 (DE-588)4151278-9 |
| title | A theory of sets |
| title_auth | A theory of sets |
| title_exact_search | A theory of sets |
| title_full | A theory of sets |
| title_fullStr | A theory of sets |
| title_full_unstemmed | A theory of sets |
| title_short | A theory of sets |
| title_sort | a theory of sets |
| topic | Logik (DE-588)4036202-4 gnd Mengenlehre (DE-588)4074715-3 gnd Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logik Mengenlehre Axiomatische Mengenlehre Mathematische Logik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000346289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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