集合论基础

Chapter 1　INTRODUCTION　1
Baby Set Theory　1
Sets-An Informal View 7
Classes　10
Axiomatic method　10
Notation　13
· · · · · · (更多)

Chapter 1　INTRODUCTION　1
Baby Set Theory　1
Sets-An Informal View 7
Classes　10
Axiomatic method　10
Notation　13
Historical Notes　14
Chatper 2　AXIOMS AND OPERATIONS　17
Axioms　17
Arbitrary Unions and Intersections　23
Algebra of Sets　27
Epilogue　33
Review Exercises　33
Chapter 3　RELATIONS AND FUNCTIONS　35
Ordered Pairs　35
Relations　39
n-Ary Relations　41
Functions　42
Infinite Cartesian Products　54
Equivalence Relations　55
Ordering Relations　62
Review Exercises　64
Chapter 4　NATURAL NUMBERS　67
Inductive Sets　67
Peano's Postulates　70
Recursion on　73
Arithmetic　79
Ordering on　83
Review Exercises　88
Chapter 5　CONSTRUCTION OF THE REAL NUMBERS　90
Integers　90
Rational Numbers　101
Real Numbers　111
Summaries　121
Two　123
Chapter 6　CARDINAL NUMBERS AND THE AXIOM OF CHIOCE　128
Equinumerosity　128
Finite Sets　133
Cardinal Arithmetic　138
Ordering Cardinal Numbers　145
Axiom of Choice　151
Countable Sets　159
Arithmetic of Infinite Cardinals　162
Continuum Hypothesis　165
Chapter 7　ORDERINGS AND ORDINALS　167
Partial Orderings　167
Well Orderings　172
Replacement Axioms　179
Epsilon-Images　182
Isomorphisms　184
Ordinal Numbers　187
Debts Paid　195
Rank　200
Chapter 8　ORDINALS AND ORDER TYPES　209
Transfinite Recursion Again　209
Alephs　212
Ordinal Operations　215
Isomorphism Types　220
Arithmetic of Order Types　222
Ordinal Arithmetic　227
Chapter 9　SPECIAL TOPICS　241
Well-Founded Relations　241
Natural Models　249
Cofinality　257
Appendix　NOTATION, LOGIC, AND PROOFS　263
Selected References for Further Study　269
List of Axioms　271
Index　273
· · · · · · (收起)