Set Theory
Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved
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Thomas Jech
Set Theory The Third Millennium Edition, revised and expanded
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Thomas Jech e-mail: [email protected]
The original edition was published in 1978 by Academic Press, Inc. in the series Pure and Applied Mathematics, vol. 79, with the ISBN 0-12-381950-4 The second edition was published in 1997 by Springer-Verlag under the same title in the series Perspectives in Mathematical Logic
Catalog-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Jech, Thomas J.: Set theory / Thomas Jech. - 3rd Millennium ed, rev. and expanded. - Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Springer monographs in mathematics) ISBN 3-540-44085-2
Mathematics Subject Classification (2000): 03Exx ISSN 1439-7382 Corrected 4th printing 2006 ISBN-10 3-540-44085-2 Springer-Verlag Berlin Heidelberg New York ISBN-13 978-3-540-44085-7 Springer-Verlag Berlin Heidelberg New York ISBN 3-540-63048-1 2nd ed. Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 1997, 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the author using a Springer TEX macro package Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper
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For Paula, Pavel, and Susanna
Preface
When I wrote the first edition in the 1970s my goal was to present the state of the art of a century old discipline that had recently undergone a revolutionary transformation. After the book was reprinted in 1997 I started contemplating a revised edition. It has soon become clear to me that in order to describe the present day set theory I would have to write a more or less new book. As a result this edition differs substantially from the 1978 book. The major difference is that the three major areas (forcing, large cardinals and descriptive set theory) are no longer treated as separate subjects. The progress in past quarter century has blurred the distinction between these areas: forcing has become an indispensable tool of every set theorist, while descriptive set theory has practically evolved into th
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