Set Theory for the Working Mathematician (Hardcover)

Krzysztof Ciesielski

ISBN 10: 0521594413 / ISBN 13: 9780521594417

Verlag: Cambridge University Press, Cambridge, 2007

Beschreibung

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 multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780521594417

Bibliografische Details

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

Verlag: Cambridge University Press, Cambridge

Erscheinungsdatum: 2007

Einband: Hardcover

Zustand: new

Über diesen Titel

Inhaltsangabe:

This 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.

Críticas:

' ... 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