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Set Theory and the Continuum Problem

Set Theory and the Continuum Problem
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作者: ,
出版社: Dover Publications
2010-03
ISBN: 9780486474847
装帧: 其他
开本: 其他
纸张: 其他
分类: 外文古旧书>英文书>语言文字
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  • A lucid, elegant, and complete survey of set theory, this volume is drawn from the authors' substantial teaching experience. The first of three parts focuses on axiomatic set theory. The second part explores the consistency of the continuum hypothesis, 目录
    Preface to the Revised 2010 Edition
    Preface
    I Axiomatic Set Theory
    1. General Background
    2. Some Basics of Class-Set Theory
    3. The Natural Numbers
    4. Superinduction, Well Ordering and Choice
    5. Ordinal Numbers
    6. Order Isomorphism and Transfinite Recursion
    7. Rank
    8. Foundation, Induction and Rank
    9. Cardinals
    II Consistency of the Continuum Hypothesis
    10. Mostowski-Shepherdson Mappings
    11. Reflection Principles
    12. Constructible Sets
    13. L is a Well-Founded First-Order Universe
    14. Constructibility is Absolute Over L
    15. Constructibility and the Continuum Hypothesis
    III Forcing and Independence Results
    16. Forcing, the Very Idea
    17. The Construction of S 4 Models for ZF
    18. The Axiom of Constructibility is Independent
    19. Independence in the Continuum Hypothesis
    20. Independence of the Axiom of Choice
    21. Constructing Classical Models
    22. Forcing Backward
    Bibliography
    Index
    List of Notation
  • 内容简介:
    A lucid, elegant, and complete survey of set theory, this volume is drawn from the authors' substantial teaching experience. The first of three parts focuses on axiomatic set theory. The second part explores the consistency of the continuum hypothesis,
  • 目录:
    目录
    Preface to the Revised 2010 Edition
    Preface
    I Axiomatic Set Theory
    1. General Background
    2. Some Basics of Class-Set Theory
    3. The Natural Numbers
    4. Superinduction, Well Ordering and Choice
    5. Ordinal Numbers
    6. Order Isomorphism and Transfinite Recursion
    7. Rank
    8. Foundation, Induction and Rank
    9. Cardinals
    II Consistency of the Continuum Hypothesis
    10. Mostowski-Shepherdson Mappings
    11. Reflection Principles
    12. Constructible Sets
    13. L is a Well-Founded First-Order Universe
    14. Constructibility is Absolute Over L
    15. Constructibility and the Continuum Hypothesis
    III Forcing and Independence Results
    16. Forcing, the Very Idea
    17. The Construction of S 4 Models for ZF
    18. The Axiom of Constructibility is Independent
    19. Independence in the Continuum Hypothesis
    20. Independence of the Axiom of Choice
    21. Constructing Classical Models
    22. Forcing Backward
    Bibliography
    Index
    List of Notation
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