# Notes on Set Theory

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xiv
2. Yiannis N. Moschovakis
Pages 1-5
3. Yiannis N. Moschovakis
Pages 7-18
4. Yiannis N. Moschovakis
Pages 19-32
5. Yiannis N. Moschovakis
Pages 33-51
6. Yiannis N. Moschovakis
Pages 53-72
7. Yiannis N. Moschovakis
Pages 73-92
8. Yiannis N. Moschovakis
Pages 93-115
9. Yiannis N. Moschovakis
Pages 117-129
10. Yiannis N. Moschovakis
Pages 131-146
11. Yiannis N. Moschovakis
Pages 147-168
12. Yiannis N. Moschovakis
Pages 169-188
13. Yiannis N. Moschovakis
Pages 189-208
14. Back Matter
Pages 209-273

### Introduction

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 ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab­ stract sets," including the Axiom of Choice, transfinite recursion, and car­ dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

### Keywords

Finite Mathematica axiom of choice language mathematics object ordinal recursion set set theory sets time transfinite induction

#### Authors and affiliations

1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

### Bibliographic information

• Book Title Notes on Set Theory
• Authors Yiannis Moschovakis
• Series Title Undergraduate Texts in Mathematics
• DOI https://doi.org/10.1007/978-1-4757-4153-7
• Copyright Information Springer-Verlag New York 1994
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-94180-6
• Softcover ISBN 978-1-4757-4155-1
• eBook ISBN 978-1-4757-4153-7
• Series ISSN 0172-6056
• Edition Number 1
• Number of Pages XIV, 273
• Number of Illustrations 6 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

## Reviews

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

From the reviews of the second edition:

"The author of this very nice introduction into the basic facts of set theory has, in this second edition modified his presentation … simplified proofs, and streamlined the terminology and notation. All the advantages of this text remained." (Siegfried J. Gottwald, Zentralblatt MATH, Vol. 1088 (14), 2006)