Classic Set Theory for Guided Independent Study

ISBN-10: 0412606100
ISBN-13: 9780412606106
Edition: 1996
Authors: Derek C. Goldrei
List price: $71.95
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Description: Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of  More...

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Book details

List price: $71.95
Copyright year: 1996
Publisher: C R C Press LLC
Publication date: 7/1/1996
Binding: Paperback
Pages: 296
Size: 8.50" wide x 10.25" long x 0.75" tall
Weight: 1.298
Language: English

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

Preface
Introduction
The Real Numbers
The Natural Numbers
The Zermelo-Fraenkel Axioms
The Axiom of Choice
Cardinals (without the Axiom of Choice)
Ordered Sets
Ordinal Numbers
Set Theory with the Axiom of Choice
Bibliography
Index

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