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集合论基础（英文版）Elements of Set Theory  |
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换货规定：从本购书中心所购买"集合论基础（英文版）Elements of Set Theory"图书如有质量问题(字迹模糊/缺页/倒装/开线/开胶/折页/封皮破损/缺少随书赠品),可在收到商品15日之内换货
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集合论是数学的一个基本分支，在数学中占据着独特的地位，其基本概念已渗透到数学的所有领域，本书从集合论中最基本的概念开始，循序渐进，深入浅出，主要内容有：公理及运算、关系与函数、自然数、实数与选择公理、秩序与序数、序数与序型等，本书附有大约300道习题。
本书可作为数学，计算机及其他相关专业本科生教材。 |
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| Chapter 1 INTRODUCTION 1 Baby Set Theory 1 Sets - An Informal View 7 Classes 10 Axiomatic method 10 Notation 13 Historical Notes 14Chatper 2 AXIOMS AND OPERATIONS 17 Axioms 17 Arbitrary Unions and Intersections 23 Algebra of Sets 27 Epilogue 33 Review Exercises 33Chapter 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 64Chapter 4 NATURAL NUMBERS 67 Inductive Sets 67 Peano's Postulates 70 Recursion on ω 73 Arithmetic 79 Ordering on ω 83 Review Exercises 88Chapter 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 200Chapter 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 227Chapter 9 SPECIAL TOPICS 241 Well-Founded Relations 241 Natural Models 249 Cofinality 257Appendix NOTATION, LOGIC, AND PROOFSSelected References for Further StudyList of AxiomsIndex |
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