# Notes on Set Theory

• Yiannis N. Moschovakis
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

• Yiannis N. Moschovakis
• 1
1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

### Bibliographic information

• 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
• Print ISBN 978-1-4757-4155-1
• Online ISBN 978-1-4757-4153-7
• Series Print ISSN 0172-6056
• Buy this book on publisher's site