Set Theory and Logic (Dover Books on Mathematics) [Paperback]

Robert R. Stoll (Author), Mathematics (Author)

Book Description

ISBN-10: 0486638294 | ISBN-13: 978-0486638294 | Publication Date: October 1, 1979

"The best introductory text we have seen." — Cosmos. Lucidly and gradually explains sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories. Its clarity makes this book excellent for self-study.

Product Details

• Paperback: 496 pages
• Publisher: Dover Publications (October 1, 1979)
• Language: English
• ISBN-10: 0486638294
• ISBN-13: 978-0486638294
• Product Dimensions: 8.2 x 5.6 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #189,022 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

57 of 58 people found the following review helpful:

4.0 out of 5 stars Incredible Best Buy, June 27, 2003

By A Customer

This review is from: Set Theory and Logic (Dover Books on Mathematics) (Paperback)

This book is without peer in its breadth of coverage of the foundations of mathematics and logic. I have given this book only 4 stars, because its treatment of any given topic
is not classic. It is the total package that astounds.
For a mere $15, you get a challenging undergraduate introduction to all of the following topics. I have written in parentheses the names of authors of more definitive treatments:

Intuitive set theory through the axiom of choice (Halmos)

Natural numbers Æ Integers Æ Rationals Æ Reals (Feferman)

Mathematical logic (Machover, Smullyan)

Metamathetics (Machover, Mendelson)

Introduction to the axiomatic approach

ZF axiomatic set theory (Suppes)

Boolean algebra through Stone's theorem and the completeness of sentential logic (Halmos & Givant)

Algebra (Birkhoff & MacLane's "Algebra")

Stoll's style is quite discursive, far from the terse lemma-theorem-corollary-remark style of so much 20th century mathematics. My only major disappointment is that the formal proof technique set out in chpt. 4 is natural deduction rather than the tableau method or Quine's Main Method.

It is indeed the case that there are no solutions to the exercises, but I do not believe that that is a major flaw.

37 of 39 people found the following review helpful:

4.0 out of 5 stars Unusually clear treatment of very abstract matters., July 29, 2001

By 

galloamericanus "galloamericanus" (Podunk, Iowa) - See all my reviews

This review is from: Set Theory and Logic (Dover Books on Mathematics) (Paperback)

This book is a great bargain: intuitive and axiomatic set theory, foundations of number systems, first order logic and its completeness and undecidability, the basics of abstract algebra, especially Boolean algebra (through the Stone theorem), elementary group theory, and Godelian incompletability. All in one inexpensive paperback. Excellent coverage of the three way crossroads where logic, modern algebra, and metamathematics intersect. Often the first reference I consult on basic logic.

Even though I am not a mathematician, I can understand, with effort, most of what the author is trying to say.

50 of 56 people found the following review helpful:

4.0 out of 5 stars Good book that falls short of being a great book., February 3, 1998

By A Customer

This review is from: Set Theory and Logic (Dover Books on Mathematics) (Paperback)

This book is very well written and easy to understand. However, it has a very serious shortcoming: there are no solutions to the exercises. If you're looking for a basic reference, this book is good, but if you want a book you can use to learn set theory and logic, get one that has solutions to the exercises.