Notes on Set Theory
Seiten
2005
|
2nd ed. 2006
Springer-Verlag New York Inc.
978-0-387-28722-5 (ISBN)
Springer-Verlag New York Inc.
978-0-387-28722-5 (ISBN)
The axiomatic theory of sets is a vibrant part of pure mathematics, and is also viewed as a foundation of mathematics. This book addresses both pure math and the fundamentals. The new edition is reworked and expanded for improved presentation.
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.
Equinumerosity.- Paradoxes and Axioms.- Are Sets All There is?.- The Natural Numbers.- Fixed Points.- Well Ordered Sets.- Choices.- Choice’s Consequences.- Baire Space.- Replacement and Other Axioms.- Ordinal Numbers.
| Erscheint lt. Verlag | 21.12.2005 |
|---|---|
| Reihe/Serie | Undergraduate Texts in Mathematics |
| Zusatzinfo | 274 Illustrations, color; 15 Illustrations, black and white; XII, 278 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-387-28722-1 / 0387287221 |
| ISBN-13 | 978-0-387-28722-5 / 9780387287225 |
| Zustand | Neuware |
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