Set Theory

1. Front Matter

   Pages I-XIV

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2. Sets

   1. Axiomatic Set Theory

      • Thomas Jech

      Pages 1-77

   2. Transitive Models of Set Theory

      • Thomas Jech

      Pages 78-136

3. More Sets

   1. Forcing and Generic Models

      • Thomas Jech

      Pages 137-215

   2. Some Applications of Forcing

      • Thomas Jech

      Pages 216-294

4. Large Sets

   1. Measurable Cardinals

      • Thomas Jech

      Pages 295-397

   2. Other Large Cardinals

      • Thomas Jech

      Pages 398-491

5. Sets of Reals

   1. Descriptive Set Theory

      • Thomas Jech

      Pages 493-578

6. Back Matter

   Pages 579-634

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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 Hierarchy of Classes, Relations, and Functions 114 15. Relative Constructibility and Ordinal Definability 126 PART II MORE SETS Chapter 3 FORCING AND GENERIC MODELS 16. Generic Models 137 17. Complete Boolean Algebras 144 18.

• Cardinal number
• Mengenlehre
• cardinals
• combinatorics
• forcing
• grosse Kardinalzahlen
• large cardinals
• mathematics
• proof
• set theory

• Department of Mathematics, The Pennsylvania State University, University Park, USA

  Thomas Jech

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