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Author Ciesielski, Krzysztof, 1957-

Title Set theory for the working mathematician / Krzysztof Ciesielski.

Published Cambridge ; New York : Cambridge University Press, [1997]


Location Call No. Status
 UniM Bund  511.322 CIES {Bund89 20200519}    AVAILABLE
Physical description xi, 236 pages ; 24 cm.
Series London Mathematical Society student texts ; 39.
London Mathematical Society student texts ; 39.
Bibliography Includes bibliographical references (pages 225-227) and index.
Contents Pt. I. Basics of set theory. 1. Axiomatic set theory. 2. Relations, functions, and Cartesian product. 3. Natural numbers, integers, and real numbers -- Pt. II. Fundamental tools of set theory. 4. Well orderings and transfinite induction. 5. Cardinal numbers -- Pt. III. The power of recursive definitions. 6. Subsets of R[superscript n]. 7. Strange real functions -- Pt. IV. When induction is too short. 8. Martin's axiom. 9. Forcing -- A. Axioms of set theory -- B. Comments on the forcing method.
Summary This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra.
The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of "modern" set theory: Martin's axiom, the diamond principle, and elements of forcing.
Written primarily as a text for beginning graduate or advanced undergraduate students, this book should also interest researchers wanting to learn more about set-theoretic techniques applicable to their fields.
Subject Set theory.
ISBN 0521594650 (paperback)
0521594413 (hardback)