Jech T., matematyka ebooki ENG
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S
pringer
M
onographs in
M
athematics
Thomas Jech
Set Theory
The Third Millennium Edition,
revised and expanded
123
Thomas Jech
e-mail:
jech@math.cas.cz
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;NewYork;HongKong;London;Milan;Paris;Tokyo:
Springer, 2002
(Springer monographs in mathematics)
ISBN 3-540-44085-2
Mathematics Subject Classif ication (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
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For Paula, Pavel, and Susanna
Preface
) under large cardinal
assumptions. Moreover, the theory of inner models has emerged as a major
part of the large cardinal theory.
The book has three parts. The first part contains material that every
student of set theory should learn and all results contain a detailed proof. In
the second part I present the topics and techniques that I believe every set
theorist should master; most proofs are included, even if some are sketchy.
For the third part I selected various results that in my opinion reflect the
state of the art of set theory at the turn of the millennium.
I wish to express my gratitude to the following institutions that made
their facilities available to me while I was writing the book: Mathematical
Institute of the Czech Academy of Sciences, The Center for Theoretical Study
in Prague, CRM in Barcelona, and the Rockefeller Foundation’s Bellagio Cen-
ter. I am also grateful to numerous set theorists who I consulted on various
subjects, and particularly to those who made invaluable comments on prelim-
inary versions of the manuscript. My special thanks are to Miroslav Repicky
who converted the handwritten manuscript to L
A
T
E
X. He also compiled the
three indexes that the reader will find extremely helpful.
Finally, and above all, I would like to thank my wife for her patience and
encouragement during the writing of this book.
R
Prague, May 2002
Thomas Jech
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 descrip-
tive 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 the study of
L
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