James E. Humphreys
Lance W. Small
2000 Mathematics Subject Classification. Primary 03Exx;
Secondary 03E30, 03E25, 03E10, 03E05.
ABSTRACT. This volume is an introduction to set theory for beginning graduate students. It covers
the basics of set theory that are considered prerequisites for other areas of mathematics such as
ordinals, cardinals, transfinite induction and recursion, and applications of Zorn's lemma. It also
contains a description of how mathematics can be founded on axiomatic set theory, as well as a
discussion of the nature of consistency results.
Library of Congress Cataloging-in-Publication Data
Just, W. (Winfried)
Discovering modern set theory / Winfried Just, Martin Weese.
p. cm. — (Graduate studies in mathematics, ISSN 1065-7339; v. 8)
Includes bibliographical references and index.
Contents: 1. The basics
ISBN 0-8218-0266-6 (v. 1 : hard cover : alk. paper)
1. Set theory. I. Weese, Martin. II. Title. III. Series.
QA248.J87 1995 95-44663
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in teaching or research. Permission is granted to quote brief passages from this publication in
reviews, provided the customary acknowledgment of the source is given.
Republication, systematic copying, or multiple reproduction of any material in this publication
is permitted only under license from the American Mathematical Society. Requests for such
permission should be addressed to the Acquisitions Department, American Mathematical Society,
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© 1996 by the American Mathematical Society. All rights reserved.
Reprinted with corrections 1998, reprinted 2008.
The American Mathematical Society retains all rights
except those granted to the United States Government.
Printed in the United States of America.
@ The paper used in this book is acid-free and falls within the guidelines
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