书目名称 | Set Theory | 编辑 | Thomas Jech | 视频video | | 丛书名称 | Perspectives in Mathematical Logic | 图书封面 |  | 描述 | The main body of this book consists of 106 numbered theorems and a dozen of examples of models of set theory. A large number of additional results is given in the exercises, which are scattered throughout the text. Most exer cises are provided with an outline of proof in square brackets [ ], and the more difficult ones are indicated by an asterisk. I am greatly indebted to all those mathematicians, too numerous to men tion by name, who in their letters, preprints, handwritten notes, lectures, seminars, and many conversations over the past decade shared with me their insight into this exciting subject. XI CONTENTS Preface xi PART I SETS Chapter 1 AXIOMATIC SET THEORY I. Axioms of Set Theory I 2. Ordinal Numbers 12 3. Cardinal Numbers 22 4. Real Numbers 29 5. The Axiom of Choice 38 6. Cardinal Arithmetic 42 7. Filters and Ideals. Closed Unbounded Sets 52 8. Singular Cardinals 61 9. The Axiom of Regularity 70 Appendix: Bernays-Godel Axiomatic Set Theory 76 Chapter 2 TRANSITIVE MODELS OF SET THEORY 10. Models of Set Theory 78 II. Transitive Models of ZF 87 12. Constructible Sets 99 13. Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis 108 14. The In Hierarch | 出版日期 | Book 19972nd edition | 关键词 | Cardinal number; Mengenlehre; cardinals; combinatorics; forcing; grosse Kardinalzahlen; large cardinals; ma | 版次 | 2 | doi | https://doi.org/10.1007/978-3-662-22400-7 | isbn_ebook | 978-3-662-22400-7Series ISSN 0172-6641 | issn_series | 0172-6641 | copyright | Springer-Verlag Berlin Heidelberg 1997 |
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