Set Theory for the Working Mathematician (Hardcover)

Krzysztof Ciesielski

ISBN 10: 0521594413 / ISBN 13: 9780521594417

Editore: Cambridge University Press, Cambridge, 2007

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Hardcover. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780521594417

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Titolo: Set Theory for the Working Mathematician (...

Casa editrice: Cambridge University Press, Cambridge

Data di pubblicazione: 2007

Legatura: Hardcover

Condizione: new

Descrizione articolo

Riassunto:

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.

Recensione:

' ... 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