Preface
엮은이의 글 

Chapter 0 Historical Introduction 1
0.1 The background of set theory 1
0.2 The paradoxes 4
0.3 The axiomatic method 6
0.4 Axiomatic set theory 13
0.5 Objections to the axiomatic approach 19
0.6 Concluding remarks 27

Chapter 1 Classes and Sets 31
1.1 Building sentences 31
1.2 Building classes 41
1.3 The algebra of classes 52
1.4 Ordered pairs and Cartesian products 58
1.5 Graphs 64
1.6 Generalized union and intersection 69
1.7 Sets 74

Chapter 2 Functions 83
2.1 Introduction 83
2.2 Fundamental concepts and de¯nitions 84
2.3 Composite and inverse functions 95
2.4 Direct images and inverse images 103
2.5 Product of a family of classes 108
2.6 The axiom of replacement 112

Chapter 3 Relations 117
3.1 Introduction 117
3.2 Fundamental concepts and de¯nitions 117
3.3 Equivalence relations and partitions 122
3.4 Pre-image, restriction and quotient 130
3.5 Equivalence relations and functions 135

Chapter 4 Partially Ordered Classes 141
4.1 Fundamental concepts and de¯nitions 141
4.2 Order preserving functions and isomorphisms 146
4.3 Distinguished elements and the duality 154
4.4 Lattices 165
4.5 Fully ordered and well-ordered 173
4.6 Isomorphism between well-ordered classes 180

Chapter 5 The Axiom of Choice 187
5.1 Introduction 187
5.2 The axiom of choice 194
5.3 An application of the axiom of choice 198
5.4 Maximal principles 203
5.5 The well-ordering theorem 206
5.6 Conclusion 209

Chapter 6 The Natural Numbers 211
6.1 Introduction 211
6.2 Elementary properties 214
6.3 Finite recursion 218
6.4 Arithmetic of natural numbers 224
6.5 Concluding remark 232

Chapter 7 Finite and Infinite Sets 235
7.1 Introduction 235
7.2 Equipotence of sets 243
7.3 Properties of in¯nite sets 246
7.4 Properties of denumerable sets 250

Chapter 8 Arithmetic of Cardinal Numbers 257
8.1 Introduction 257
8.2 Operations on cardinal numbers 260
8.3 Ordering of the cardinal numbers 266
8.4 Infinite cardinal numbers 272
8.5 Infinite sums and products 276
 

Chapter 9 Arithmetic of Ordinal Numbers 281
9.1 Introduction 281
9.2 Operations on ordinal numbers 286
9.3 Ordering of the ordinal numbers 292
9.4 The alephs and the continuum hypothesis 301
9.5 Construction of the ordinals and cardinals¤ 305

Chapter 10 Transfinite Recursion and Selected Topics 315
10.1 Transfinite recursion 315
10.2 Properties of ordinal exponentiation 323
10.3 Normal form 330
10.4 Epsilon numbers 336
10.5 Inaccessible ordinals and cardinals 342

Chapter 역사적 소개 355
0.1 집합론의 배경 355
0.2 역설 357
0.3 공리적 방법 360
0.4 공리적 집합론 366
0.5 공리적 집합론에 대한 반론과 다른 대안들 373
0.6 맺음말 380

Bibliography 383
Index 385

지은이: Charles C. Pinter 

엮은이: 박찬녕

배송정보

교환/반품 정보