Book:Keith J. Devlin/Fundamentals of Contemporary Set Theory
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Keith J. Devlin: Fundamentals of Contemporary Set Theory
Published $\text {1979}$, Springer Verlag
- ISBN 978-0-387-90441-2
Subject Matter
Contents
- CHAPTER I. NAIVE SET THEORY
- 1. What is a set?
- 2. Operations on sets.
- 3. Notation for sets.
- 4. Sets of sets.
- 5. Relations.
- 6. Functions.
- 7. Well-orderings and ordinals.
- CHAPTER II. THE ZERMELO-FRAENKEL AXIOMS
- 1. The language of set theory.
- 2. The cumulative hierarchy of sets.
- 3. Zermelo-Fraenkel set theory.
- 4. Axioms for set theory.
- 5. Summary of the Zermelo-Fraenkel axioms
- 6. Classes.
- 7. Set theory as an axiomatic theory.
- 8. The recursion principle.
- 9. The axiom of choice.
- CHAPTER III. ORDINAL AND CARDINAL NUMBERS
- 1. Ordinal numbers.
- 2. Addition of ordinals.
- 3. Multiplication of ordinals.
- 4. Sequences of ordinals.
- 5. Ordinal exponentiation.
- 6. Cardinality. Cardinal numbers.
- 7. Arithmetic of cardinal numbers.
- 8. Cofinality. Singular and regular cardinals.
- 9. Cardinal exponentiation.
- 10. Inaccessible cardinals.
- CHAPTER IV. SOME TOPICS IN PURE SET THEORY.
- 1. The Borel hierarchy.
- 2. Closed unbounded sets.
- 3. Stationary sets and regressive functions.
- 4. Trees.
- 5. Extensions of Lebesgue measure.
- 6. A result about the GCH.
- CHAPTER V. THE AXIOM OF CONSTRUCTIBILITY.
- 1. Constructible sets.
- 2. The constructible hierarchy.
- 3. The axiom of constructibility.
- 4. The consistency of constructible set theory.
- 5. Use of the axiom of constructibility.
- CHAPTER VI. INDEPENDENCE PROOFS IN SET THEORY.
- 1. Some examples of undecidable statements.
- 2. The idea of a boolean-valued universe.
- 3. The boolean-valued universe.
- 4. $V^{\Bbb B}$ and $V$.
- 5. Boolean-valued sets and independence proofs.
- 6. The non-provability of CH.
- BIBLIOGRAPHY
- GLOSSARY OF NOTATION
- INDEX