Notes on Set Theory
What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1994, 1994
|
| Edition: | 1st ed. 1994 |
| Series: | Undergraduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Introduction
- 2. Equinumerosity
- 3. Paradoxes and axioms
- 4. Are sets all there is?
- 5. The natural numbers
- 6. Fixed points
- 7. Well ordered sets
- 8. Choices
- 9. Choice’s consequences
- 10. Baire space
- 11. Replacement and other axioms
- 12. Ordinal numbers
- A. The real numbers
- Congruences
- Fields
- Ordered fields
- Uniqueness of the rationals
- Existence of the rationals
- Countable, dense, linear orderings
- The archimedean property
- Nested interval property
- Dedekind cuts
- Existence of the real numbers
- Uniqueness of the real numbers
- Problems for Appendix A
- B. Axioms and universes
- Set universes
- Propositions and relativizations
- Rieger universes
- Rieger’s Theorem
- Bisimulations
- The antifounded universe
- Aczel’s Theorem
- Problems for Appendix B.