Intermediate set theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 234 S. |
| ISBN: | 0471964948 0471964964 |
Staff View
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Record in the Search Index
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| adam_text | INTERMEDIATE SET THEORY F. R. DRAKE UNIVERSITY OF LEEDS, UK D. SINGH
INDIAN INSTITUE OF TECHNOLOGY, BOMBAY, INDIA JOHN WILEY & SONS
CHICHESTER * NEW YORK * BRISBANE * TORONTO * SINGAPORE CONTENTS 1 SOME
OF THE HISTORY OF THE CONCEPT OF SETS 1 1.1 CANTOR S CONTRIBUTION 1 1.2
CANTOR S CONCEPT OF A SET 3 1.3 PARADOXES 5 1.4 TYPE STRUCTURES 7 1.5
CULMINATION INTO AXIOMATICS . , 10 2 FIRST-ORDER LOGIC AND ITS USE IN
SET THEORY 13 2.1 INTRODUCTION 13 2.2 THE SYNTAX OF LST 14 2.3 PROOFS
AND DERIVATIONS IN LST 18 2.4 SEMANTICS OF LST 19 2.5 ADDING NEW TERMS
24 3 THE AXIOMS OF SET THEORY 27 3.1 THE ZERMELO-FRAENKEL AXIOMS 27 3.2
ARGUMENTS FOR THESE AXIOMS 31 4 CARDINALS 37 4.1 COUNTABLE SETS 37 4.2
UNCOUNTABLE SETS 41 4.3 THE ARITHMETIC OF CARDINAL NUMBERS 46 5 ORDER
RELATIONS AND ORDERED SETS 51 5.1 ORDERINGS 51 5.2 SOME PROPERTIES OF
ORDERED SETS 53 5.3 LATTICES AND BOOLEAN ALGEBRAS 56 5.4 WELL-ORDERED
SETS 66 6 DEVELOPING MATHEMATICS WITHIN ZFC 7 1 6.1 THE NATURAL NUMBERS
71 VIII INTERMEDIATE SET THEORY 6.2 THE PEANO AXIOMS FOR THE NATURAL
NUMBERS 76 6.3 THE RATIONAL NUMBERS 85 6.4 THE REAL NUMBERS 89 6.5 ~
ORDINALS IN ZF: BASIC PROPERTIES 93 6.6 TRANSFINITE INDUCTION 97 6.7
CARDINALS AS INITIAL ORDINALS 105 7 THE AXIOM OF CHOICE 109 7.1 SIMPLE
FORMS 109 7.2 THE WELL-ORDERING THEOREM 112 7.3 MAXIMAL PRINCIPLES AND
ZORN S LEMMA 114 7.4 SIMPLE CONSEQUENCES OF THE AXIOM OF CHOICE 117 8
CONSTRUCTIBLE SETS AND FORCING 127 8.1 GODEL S CONSTRUCTIBLE SETS 128
8.2 THE DEFINITION OF L 133 8.3 REFLECTION PRINCIPLES 138 8.4 PROPERTIES
OF L 140 8.5 THE AXIOM OF CHOICE IN L 145 8.6 THE GENERALIZED CONTINUUM
HYPOTHESIS IN L 148 8.7 ANOTHER PRESENTATION 153 8.8 FORCING MODELS 154
8.9 FORCING IN PRACTICE: THE ZFC AXIOMS HOLD IN M[G] 159 8.10 FORCING IN
PRACTICE: SOME MODELS 164 8.11 PROOFS OF THE DEFINABILITY AND TRUTH
LEMMAS 171 8.12 MODELS FOR THE INDEPENDENCE OF THE AXIOM OF CHOICE 179
8.13 A MODEL WITH A DEDEKIND-FINITE SET 184 8.14 BOOLEAN-VALUED MODELS:
ANOTHER PRESENTATION 189 9 MISCELLANEOUS FURTHER TOPICS 19 3 9.1
INTRODUCING VARIABLES FOR CLASSES 193 9.2 SYSTEM VNB 193 9.3 SYSTEM MK
197 9.4 AXIOMS OF EXTENT 199 9.5 OTHER PRESENTATIONS OF SET THEORY 202
9.6 REMARKS ON THE PHILOSOPHY OF MATHEMATICS 207 10 APPENDIX: SOME BASIC
DEFINITIONS 213 10.1 SIMPLEST CONSTRUCTIONS, AND VARIANTS 213 10.2
ORDERED PAIRS, RELATIONS, FUNCTIONS, FAMILIES AND SEQUENCES . . . 214
REFERENCES 219 INDEX 225
|
| any_adam_object | 1 |
| author | Drake, F. R. 1936- Singh, Dasharath |
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| author_facet | Drake, F. R. 1936- Singh, Dasharath |
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| callnumber-raw | QA248.D727 1996 |
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| dewey-full | 511.3/22 511.3/2221 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511.3/22 511.3/22 21 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:38Z |
| institution | BVB |
| isbn | 0471964948 0471964964 |
| language | English |
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| physical | X, 234 S. |
| publishDate | 1996 |
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| publisher | Wiley |
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| spelling | Drake, F. R. 1936- Verfasser (DE-588)1045657808 aut Intermediate set theory F. R. Drake ; D. Singh Chichester [u.a.] Wiley 1996 X, 234 S. txt rdacontent n rdamedia nc rdacarrier Verzamelingen (wiskunde) gtt Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 Singh, Dasharath Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007421268&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Drake, F. R. 1936- Singh, Dasharath Intermediate set theory Verzamelingen (wiskunde) gtt Set theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Intermediate set theory |
| title_auth | Intermediate set theory |
| title_exact_search | Intermediate set theory |
| title_full | Intermediate set theory F. R. Drake ; D. Singh |
| title_fullStr | Intermediate set theory F. R. Drake ; D. Singh |
| title_full_unstemmed | Intermediate set theory F. R. Drake ; D. Singh |
| title_short | Intermediate set theory |
| title_sort | intermediate set theory |
| topic | Verzamelingen (wiskunde) gtt Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Verzamelingen (wiskunde) Set theory Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007421268&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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