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London Mathematical Society Student Texts: Set Theory for the Working Mathematician by Krzysztof Ciesielski (1997, Trade Paperback)
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521594650
ISBN-139780521594653
eBay Product ID (ePID)417266
Product Key Features
Number of Pages252 Pages
Publication NameSet Theory for the Working Mathematician
LanguageEnglish
SubjectSet Theory, Logic
Publication Year1997
TypeTextbook
Subject AreaMathematics
AuthorKrzysztof Ciesielski
SeriesLondon Mathematical Society Student Texts
FormatTrade Paperback
Dimensions
Item Height0.6 in
Item Weight12.2 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN97-010533
Reviews' ... the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.' Ian Tweddle, Proceedings of the Edinburgh Mathematical Society, "...a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it." Proceedings of the Edinburgh Mathematical Society, ' … the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.' Ian Tweddle, Proceedings of the Edinburgh Mathematical Society, "The book contains a large amount of interesting and well-presented material on transfinite recursion and transfinite induction and a very good introduction to Martin's axiom. The short discussion of forcing can give the reader a first glimplse at the method. The treatment of mathematical logic is too sketchy to be of any realuse and may be a source of confusion." Journal of Symbolic Logic, ‘ … the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.’Ian Tweddle, Proceedings of the Edinburgh Mathematical Society, ' ... the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.'Ian Tweddle, Proceedings of the Edinburgh Mathematical Society
Dewey Edition21
Series Volume NumberSeries Number 39
IllustratedYes
Dewey Decimal511.3/22
Table Of ContentPart I. Basics of Set Theory: 1. Axiomatic set theory; 2. Relations, functions and Cartesian product; 3. Natural, integer and real numbers; Part II. Fundamental Tools of Set Theory: 4. Well orderings and transfinite induction; 5. Cardinal numbers; Part III. The Power of Recursive Definitions: 6. Subsets of Rn; 7. Strange real functions; Part IV. When Induction is Too Short: 8. Martin's axiom; 9. Forcing; Part V. Appendices: A. Axioms of set theory; B. Comments on forcing method; C. Notation.
SynopsisThis text concentrates on the typical methods of modern set theory: transfinite induction, Zorn's Lemma, the Continuum Hypothesis, Martin's Axiom, the Diamond Principle and elements of forcing. It supplies students and researchers with the tools most applicable to other areas of pure mathematics, such as abstract geometry, real analysis, topology, and algebra., 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 level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields., 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 level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.
LC Classification NumberQA248 .C475 1997
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