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Titlebook: Set Theory; Thomas Jech Book 19972nd edition Springer-Verlag Berlin Heidelberg 1997 Cardinal number.Mengenlehre.cardinals.combinatorics.fo

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发表于 2025-3-21 17:11:33 | 显示全部楼层 |阅读模式
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Titlebook: Set Theory;  Thomas Jech Book 19972nd edition Springer-Verlag Berlin Heidelberg 1997 Cardinal number.Mengenlehre.cardinals.combinatorics.fo
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
doihttps://doi.org/10.1007/978-3-662-22400-7
isbn_ebook978-3-662-22400-7Series ISSN 0172-6641
issn_series 0172-6641
copyrightSpringer-Verlag Berlin Heidelberg 1997
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0172-6641 esults 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, wh
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Forcing and Generic Modelsansitive model of set theory, namely the constructible universe .. And . satisfies the generalized continuum hypothesis. Thus if we wish to show, e.g., that the continuum hypothesis is unprovable in ZFC we cannot just look for a transitive model ? that would satisfy 2. > N.. What is needed is a diff
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Descriptive Set Theory images of closed sets) or are definable in a simple way. The main theme is that questions that are difficult to answer if asked for arbitrary sets of reals, become much easier when asked for sets that have a simple description. An example of that is the Cantor-Bendixson theorem (Theorem 14): Every
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Forcing and Generic Models, that the continuum hypothesis is unprovable in ZFC we cannot just look for a transitive model ? that would satisfy 2. > N.. What is needed is a different way of constructing models of set theory. There are several possible approaches to this problem:
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Springer-Verlag Berlin Heidelberg 1997
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Axiomatic Set TheoryIf X and Y have the same elements, then X = Y.
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