Set theory for the working mathematician [EBook] / Krzysztof Ciesielski.
Set theory for the working mathematician [EBook] / Krzysztof Ciesielski.
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,...
Personal Name(s):  Ciesielski, Krzysztof, (author) 

Imprint: 
Cambridge :
Cambridge University Press,
1997

Physical Description: 
1 online resource (xi, 236 pages) 
Note: 
englisch 
ISBN: 
9781139173131 9780521594653 9780521594417 
Series Title: 
London Mathematical Society student texts ;
39 
Subject (LOC):  
Full Text 
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. 