Introduction to Set Theory, Revised and Expanded (Chapman & Hall/CRC Pure and Applied Mathematics) 3rd Edition
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". . .a fine text. . ..The proofs are both elegant and readable. "
---American Mathematical Monthly
". . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material. "
". . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments. "
---The Mathematical Intelligencer
"The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers. "
---Quarterly Review of Applied Mathematics
". . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added. "
- ASIN : 0824779150
- Publisher : Marcel Dekker; 3rd edition (June 22, 1999)
- Language : English
- Hardcover : 310 pages
- ISBN-10 : 9780824779153
- ISBN-13 : 978-0824779153
- Item Weight : 1.25 pounds
- Dimensions : 6 x 0.75 x 9 inches
- Best Sellers Rank: #307,756 in Books (See Top 100 in Books)
- Customer Reviews:
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Not for the casual reader or a beginner.
The reader should be prepared to engage the material
at a mathematically serious level to profit from it.
The exposition is exemplary; the material well organized.
Plenty of exercises for the student.
Goldrei's text is also very good for self-study,
but this book covers much more ground.
The pace is leisurely with a close look at the details. The axiom of choice is used only when necessary and it's uses are highlighted. The exercises contain real meat but are broken up in handable pieces. They also give alternative approaches to topics treated in the main text. Solutions are not contained.
The last section is devoted to an outlook at more advanced set theory. The ideas of the constructible universe and of forcing are outlined, as far as that is possible on that level. There is also a discussion on candidates for additional axioms.
The reader will gain both insight into what set theory is and how powerful it is. There is no better book for the same audience.