006 Notes on Set Theory.pdf

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Undergraduate Texts in Mathematics
Editors
S. Axler
K.A. Ribet
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Undergraduate Texts in Mathematics
Abbott: Understanding Analysis.
Anglin: Mathematics: A Concise
History and Philosophy.
Readings in Mathematics .
Anglin/Lambek: The Heritage of
Thales.
Readings in Mathematics .
Apostol: Introduction to Analytic
Number Theory. Second edition.
Armstrong: Basic Topology.
Armstrong: Groups and Symmetry.
Axler: Linear Algebra Done Right.
Second edition.
Beardon: Limits: A New Approach to
Real Analysis.
Bak/Newman: Complex Analysis.
Second edition.
Banchoff/Wermer: Linear Algebra
Through Geometry. Second edi-
tion.
Berberian: A First Course in Real
Analysis.
Bix: Conics and Cubics: A Concrete
Introduction to Algebraic Curves.
Brèmaud: An Introduction to
Probabilistic Modeling.
Bressoud: Factorization and
Primality Testing.
Bressoud: Second Year Calculus.
Readings in Mathematics .
Brickman: Mathematical
Introduction to Linear
Programming and Game Theory.
Browder: Mathematical Analysis: An
Introduction.
Buchmann: Introduction to
Cryptography. Second Edition.
Buskes/van Rooij: Topological
Spaces: From Distance to
Neighborhood.
Callahan: The Geometry of
Spacetime: An Introduction to
Special and General Relavitity.
Carter/van Brunt: The Lebesgue–
Stieltjes Integral: A Practical
Introduction.
Cederberg: A Course in Modern
Geometries. Second edition.
Chambert-Loir: A Field Guide to
Algebra
Childs: A Concrete Introduction to
Higher Algebra. Second edition.
Chung/AitSahlia: Elementary
Probability Theory: With
Stochastic Processes and an
Introduction to Mathematical
Finance. Fourth edition.
Cox/Little/O’Shea: Ideals, Varieties,
and Algorithms. Second edition.
Croom: Basic Concepts of Algebraic
Topology.
Cull/Flahive/Robson: Difference
Equations. From Rabbits to Chaos
Curtis: Linear Algebra: An
Introductory Approach. Fourth
edition.
Daepp/Gorkin: Reading, Writing,
and Proving: A Closer Look at
Mathematics.
Devlin: The Joy of Sets:
Fundamentals of Contemporary
Set Theory. Second edition.
Dixmier: General Topology.
Driver: Why Math?
Ebbinghaus/Flum/Thomas:
Mathematical Logic. Second edition.
Edgar: Measure, Topology, and
Fractal Geometry.
Elaydi: An Introduction to
Difference Equations. Third
edition.
Erdõs/Surányi: Topics in the
Theory of Numbers.
Estep: Practical Analysis on One
Variable.
Exner: An Accompaniment to
Higher Mathematics.
Exner: Inside Calculus.
Fine/Rosenberger: The
Fundamental Theory of Algebra.
Fischer: Intermediate Real Analysis.
Flanigan/Kazdan: Calculus Two:
Linear and Nonlinear Functions.
Second edition.
Fleming: Functions of Several
Variables. Second edition.
Foulds: Combinatorial Optimization
for Undergraduates.
Foulds: Optimization Techniques:
An Introduction.
(continued after index)
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Yiannis Moschovakis
Notes on Set Theory
Second Edition
With 48 Figures
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Yiannis Moschovakis
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA 90095-1555
USA
ynm@math.ucla.edu
Editorial Board
S. Axler
K.A. Ribet
Mathematics Department
Mathematics Department
San Francisco State
University of California,
University
Berkeley
San Francisco, CA 94132
Berkeley, CA 94720-3840
USA
USA
axler@sfsu.edu
ribet@math.berkeley.edu
Mathematics Subject Classification (2000): 03-01, 03Exx
Library of Congress Control Number: 2005932090 (hardcover)
Library of Congress Control Number: 2005933766 (softcover)
ISBN-10: 0-387-28722-1 (hardcover)
ISBN-13: 978-0387-28722-5 (hardcover)
ISBN-10: 0-387-28723-X (softcover)
ISBN-13: 978-0387-28723-2 (softcover)
Printed on acid-free paper.
© 2006 Springer Science+Business Media, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without
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