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Set theory /
This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appen...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Hungarian |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1999.
|
| Edición: | 1st English ed. |
| Colección: | London Mathematical Society student texts ;
48. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Definition of equivalence. The concept of cardinality. The Axiom of Choice
- Countable cardinal, continuum cardinal
- Comparison of cardinals
- Operations with sets and cardinals
- Ordered sets. Order types. Ordinals
- Properties of wellordered sets. Good sets. The ordinal operation
- Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem
- Definition of the cardinality operation. Properties of cardinalities. The cofinality operation
- Properties of the power operation
- Hints for solving problems marked with * in Part I
- An axiomatic development of set theory
- The Zermelo-Fraenkel axiom system of set theory
- Definition of concepts; extension of the language
- A sketch of the development. Metatheorems
- A sketch of the development. Definitions of simple operations and properties (continued)
- A sketch of the development. Basic theorems, the introduction of [omega] and R (continued)
- The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7
- The role of the Axiom of Regularity
- Proofs of relative consistency. The method of interpretation
- Proofs of relative consistency. The method of models
- Topics in combinatorial set theory
- Stationary sets
- [Delta]-systems
- Ramsey's Theorem and its generalizations. Partition calculus
- Inaccessible cardinals. Mahlo cardinals
- Measurable cardinals
- Real-valued measurable cardinals, saturated ideals
- Weakly compact and Ramsey cardinals
- Set mappings.