**Graduate Studies in Mathematics**

Volume: 8;
1996;
210 pp;
Hardcover

MSC: Primary 03;

Print ISBN: 978-0-8218-0266-3

Product Code: GSM/8

List Price: $48.00

AMS Member Price: $38.40

MAA Member Price: $43.20

**Electronic ISBN: 978-1-4704-2068-0
Product Code: GSM/8.E**

List Price: $48.00

AMS Member Price: $38.40

MAA Member Price: $43.20

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# Discovering Modern Set Theory. I: The Basics

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*Winfried Just; Martin Weese*

This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.

#### Readership

Graduate students and mathematicians interested in set-theoretical techniques.

#### Reviews & Endorsements

These books aim to support first courses in rigorous set theory … are thoroughly competent: well-organized, scrupulous in pointing out both mathematical and philosophical difficulties, carefully graded from relatively straightforward beginnings to demanding conclusions. The more interesting, and more demanding, approach is that of Just and Weese. These books are for those who not only want to learn mathematics, but want to think about mathematics.

-- Bulletin of the London Mathematical Society

Well written and userfriendly.

-- Zentralblatt MATH

Serious graduate students … would profit from reading the book for the mathematical maturity they would gain in the process. The conversational, almost Socratic, style of exposition is well suited to giving students some insight into the process of doing mathematics as well as to the importance of asking the right questions … Just and Weese's text would be ideally suited for … students who are serious about studying set theory.

-- Journal of Symbolic Logic

The careful exposition, written in a lively and very readable style which addresses the reader rather directly, provides (by explanations, comments, and remarks) much information and motivation. Recommended.

-- Monatshefte für Mathematik

#### Table of Contents

# Table of Contents

## Discovering Modern Set Theory. I: The Basics

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents ix10 free
- Preface xi12 free
- How to Read this Book xiii14 free
- Basic Notations xvii18 free
- Introduction 120 free
- Part 1. Not Entirely Naive Set Theory 928 free
- Part 2. An Axiomatic Foundation of Set Theory 6988
- Chapter 5. Formal Languages and Models 7190
- Chapter 6. Power and Limitations of the Axiomatic Method 81100
- Chapter 7. The Axioms 107126
- Chapter 8. Classes 121140
- Chapter 9. Versions of the Axiom of Choice 129148
- Chapter 10. The Ordinals 155174
- Chapter 11. The Cardinals 173192
- Chapter 12. Pictures of the Universe 187206

- Subject Index 205224
- Index of Notation 209228 free
- Back Cover Back Cover1230