Customer Reviews

Set Theory and Logic (Dover Books on Mathematics)

5 star:		(1)
4 star:		(3)
3 star:		(3)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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.

If you are already familiar with the material, this book is a concise and clear reference, and yes a great buy. But for learning these topics from the beginning, you would be better served by other books that are focused on just a particular topic.

For example, for logic in the context of set theory, I highly recommend Daniel Velleman's How to Prove it.

It is really more about foundational issues than sets and logic. The preface says this was intended as a one-year course in the foundations of math for upper division math majors. The delivery is slow and gentle, rather wordy, and a bit stodgy -- not always crystal clear about what point he is making. It is suitable for students who have no experience with higher math. I don't know about students at the author's school, but I think it would try the patience of most seniors or grad students in math. I would recommend it more to lower division and philosophy majors.

This is a good book for an introductory course on the subject. It contains the basic topics, but if you are looking for strong introduction to mathematical logic, maybe this is not a good choice. In any case, you can take it for granted since contains a very good selection of topics and perhaps you can support it with other books.

I've gone through a number of introductory books on set theory. This one is definitely my favourite. The coverage of the material, and way it is presented for a beginner on the subject is the best I've seen. Other reviewers have mentioned that Stoll doesn't have answers to the exercise problems. This isn't a problem, Stoll covers enough detail with explanations and examples that you shouldn't have any problems with the exercises.