This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Author(s): Herbert B. Enderton
Edition: 1
Publisher: Academic Press
Year: 1977
Language: English
Pages: 289
Contents......Page 4
Preface......Page 7
List of Symbols......Page 9
Baby set theory......Page 11
Sets - an informal view......Page 17
Axiomatic method......Page 20
Notation......Page 23
Historical notes......Page 24
Axioms......Page 27
Arbitrary unions and intersections......Page 33
Algebra of sets......Page 37
Epilogue......Page 43
Ordered pairs......Page 45
Relations......Page 49
n-ary relations......Page 51
Functions......Page 52
Infinite cartesian products......Page 64
Equivalence relations......Page 65
Ordering relations......Page 72
4. Natural Numbers......Page 76
Inductive sets......Page 77
Peano's postulates......Page 80
Recursion on ω......Page 83
Arithmetic......Page 89
Ordering on ω......Page 93
Integers......Page 100
Rational numbers......Page 111
Real numbers......Page 121
Summaries......Page 131
Two......Page 133
Equinumerosity......Page 138
Finite sets......Page 143
Cardinal arithmetic......Page 148
Ordering cardinal numbers......Page 155
Axiom of choice......Page 161
Countable sets......Page 169
Arithmetic of infinite cardinals......Page 172
Continuum hypothesis......Page 175
Partial orderings......Page 177
Well orderings......Page 182
Replacement axioms......Page 189
Epsilon-images......Page 192
Isomorphisms......Page 194
Ordinal numbers......Page 197
Debts paid......Page 205
Rank......Page 210
Transfinite recursion again......Page 219
Alephs......Page 222
Ordinal operations......Page 225
Isomorphism types......Page 230
Ordinal arithmetic......Page 237
Well-founded relations......Page 251
Natural models......Page 259
Cofinality......Page 267
Appendix: Notation, Logic and Proofs......Page 273
Selected References for Further Study......Page 279
List of Axioms......Page 281
Index......Page 283
