Introduction to set theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1999
|
| Ausgabe: | 3. ed., rev. and expanded |
| Schriftenreihe: | Pure and applied mathematics
220 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 291 S. graph. Darst. |
| ISBN: | 0824779150 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804127420390834176 |
|---|---|
| adam_text | INTRODUCTION TO SET THEORY THIRD EDITION, REVISED AND EXPANDED KAREL
HRBACEK THE CITY COLLEGE OF THE CITY UNIVERSITY OF NEW YORK NEW YORK,
NEW YORK THOMAS JECH THE PENNSYLVANIA STATE UNIVERSITY UNIVERSITY PARK,
PENNSYLVANIA MARCEL MARCEL DEKKER, INC. NEW YORK * BASEL CONTENTS
PREFACE TO THE THIRD EDITION III PREFACE TO THE SECOND EDITION V 1 SETS
1 1 INTRODUCTION TO SETS 1 2 PROPERTIES 3 3 THE AXIOMS 7 4 ELEMENTARY
OPERATIONS ON SETS 12 2 RELATIONS, FUNCTIONS, AND ORDERINGS 17 1 ORDERED
PAIRS 17 2 RELATIONS 18 3 FUNCTIONS 23 4 EQUIVALENCES AND PARTITIONS 29
5 ORDERINGS 33 3 NATURAL NUMBERS 39 1 INTRODUCTION TO NATURAL NUMBERS 39
2 PROPERTIES OF NATURAL NUMBERS 42 3 THE RECURSION THEOREM 46 4
ARITHMETIC OF NATURAL NUMBERS 52 5 OPERATIONS AND STRUCTURES 55 4
FINITE, COUNTABLE, AND UNCOUNTABLE SETS 65 1 CARDINALITY OF SETS 65 2
FINITE SETS 69 3 COUNTABLE SETS 74 4 LINEAR ORDERINGS 79 5 COMPLETE
LINEAR ORDERINGS 86 6 UNCOUNTABLE SETS 90 5 CARDINAL NUMBERS 93 1
CARDINAL ARITHMETIC 93 2 THE CARDINALITY OF THE CONTINUUM 98 VII VIII
CONTENTS 6 ORDINAL NUMBERS 103 1 WEIL-ORDERED SETS 103 2 ORDINAL NUMBERS
107 3 THE AXIOM OF REPLACEMENT ILL 4 TRANSFINITE INDUCTION AND RECURSION
114 5 ORDINAL ARITHMETIC 119 6 THE NORMAL FORM 124 7 ALEPHS 129 1
INITIAL ORDINALS 129 2 ADDITION AND MULTIPLICATION OF ALEPHS 133 8 THE
AXIOM OF CHOICE 137 1 THE AXIOM OF CHOICE AND ITS EQUIVALENTS 137 2 THE
USE OF THE AXIOM OF CHOICE IN MATHEMATICS 144 9 ARITHMETIC OF CARDINAL
NUMBERS 155 1 INFINITE SUMS AND PRODUCTS OF CARDINAL NUMBERS 155 2
REGULAR AND SINGULAR CARDINALS 160 3 EXPONENTIATION OF CARDINALS 164 10
SETS OF REAL NUMBERS 171 1 INTEGERS AND RATIONAL NUMBERS 171 2 REAL
NUMBERS 175 3 TOPOLOGY OF THE REAL LINE 179 4 SETS OF REAL NUMBERS 188 5
BOREL SETS 194 11 FILTERS AND ULTRAFLLTERS 201 1 FILTERS AND IDEALS 201
2 ULTRAFILTERS 205 3 CLOSED UNBOUNDED AND STATIONARY SETS 208 4 SILVER S
THEOREM 212 12 COMBINATORIAL SET THEORY 217 1 RAMSEY S THEOREMS 217 2
PARTITION CALCULUS FOR UNCOUNTABLE CARDINALS 221 3 TREES 225 4 SUSLIN S
PROBLEM 230 5 COMBINATORIAL PRINCIPLES 233 13 LARGE CARDINALS 241 1 THE
MEASURE PROBLEM 241 2 LARGE CARDINALS 246 CONTENTS IX 14 THE AXIOM OF
FOUNDATION 251 1 WEIL-FOUNDED RELATIONS 251 2 WEIL-FOUNDED SETS 256 3
NON-WELL-FOUNDED SETS 260 15 THE AXIOMATIC SET THEORY 267 1 THE
ZERMELO-FRAENKEL SET THEORY WITH CHOICE 267 2 CONSISTENCY AND
INDEPENDENCE 270 3 THE UNIVERSE OF SET THEORY 277 BIBLIOGRAPHY 285 INDEX
286
|
| any_adam_object | 1 |
| author | Hrbacek, Karel Jech, Thomas J. 1944- |
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| classification_rvk | CC 2400 SK 150 |
| ctrlnum | (OCoLC)246209678 (DE-599)BVBBV012754049 |
| dewey-full | 511.322 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.322 |
| dewey-search | 511.322 |
| dewey-sort | 3511.322 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 3. ed., rev. and expanded |
| format | Book |
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| isbn | 0824779150 |
| language | English |
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| physical | IX, 291 S. graph. Darst. |
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| spelling | Hrbacek, Karel Verfasser aut Introduction to set theory Karel Hrbacek ; Thomas J. Jech 3. ed., rev. and expanded New York [u.a.] Dekker 1999 IX, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 220 Axiomatische Mengenlehre Axiomatische Mengenlehre (DE-588)4143743-3 gnd rswk-swf 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 Axiomatische Mengenlehre (DE-588)4143743-3 s 2\p DE-604 Jech, Thomas J. 1944- Verfasser (DE-588)107482673 aut Pure and applied mathematics 220 (DE-604)BV000001885 220 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008671751&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hrbacek, Karel Jech, Thomas J. 1944- Introduction to set theory Pure and applied mathematics Axiomatische Mengenlehre Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd |
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| title | Introduction to set theory |
| title_auth | Introduction to set theory |
| title_exact_search | Introduction to set theory |
| title_full | Introduction to set theory Karel Hrbacek ; Thomas J. Jech |
| title_fullStr | Introduction to set theory Karel Hrbacek ; Thomas J. Jech |
| title_full_unstemmed | Introduction to set theory Karel Hrbacek ; Thomas J. Jech |
| title_short | Introduction to set theory |
| title_sort | introduction to set theory |
| topic | Axiomatische Mengenlehre Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Axiomatische Mengenlehre Mengenlehre Einführung |
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