Author | Devlin, Keith J. author |
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Title | Fundamentals of Contemporary Set Theory [electronic resource] / by Keith J. Devlin |
Imprint | New York, NY : Springer US, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0084-7 |
Descript | online resource |
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. -- 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. -- 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. -- 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. -- 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. -- 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. VB and V. -- 5. Boolean-valued sets and independence proofs. -- 6. The non-provability of CH. -- GLOSSARY OF NOTATION