Notes on Set Theory (Undergraduate Texts in Mathematics) - Softcover

Moschovakis, Yiannis

Softcover

ISBN 10: 038728723X ISBN 13: 9780387287232

Publisher: Springer, 2005

Synopsis

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects: it 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 book is geared to advanced undergraduate or beginning graduate mathematics students and mathematically minded graduate students in computer science and philosophy.

About this title

Review

About the First Edition:

This is a sophisticated undergraduate set theory text, brimming with mathematics, and packed with elegant proofs, historical explanations, and enlightening exercises, all presented at just the right level for a first course in set theory.
- Joel David Hamkins, Journal of Symbolic Logic

This is an excellent introduction to axiomatic set theory, viewed both as a foundation of mathematics and as a branch of mathematics with its own subject matter, basic results, open problems.
- Achille C. Varzi, History and Philosophy of Logic

Synopsis

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author added solutions to the exercises, and rearranged and reworked the text in several places to improve the presentation. The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy.

Edition details

• Publisher: Springer
• Publication date: 2005
• Language: English
• ISBN 10: 038728723X
• ISBN 13: 9780387287232
• Binding: Paperback
• Edition number: 2
• Number of pages: 290