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Title: Set Theory and Logic by Robert R. Stoll ISBN: 0-486-63829-4 Publisher: Dover Pubns Pub. Date: 01 October, 1979 Format: Paperback Volumes: 1 List Price(USD): $18.95 |
Average Customer Rating: 4 (3 reviews)
Rating: 4
Summary: Incredible Best Buy
Comment: 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.
Rating: 4
Summary: Unusually clear treatment of very abstract matters.
Comment: I am not a mathematician. Even so, I can understand, with effort a lot of what the author is trying to say. The choice of topics is outstanding. Excellent coverage of the three way crossroads where logic, modern algebra, and metamathematics intersect.
Rating: 4
Summary: Good book that falls short of being a great book.
Comment: 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.
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Title: Axiomatic Set Theory by Patrick Suppes ISBN: 0486616304 Publisher: Dover Pubns Pub. Date: 01 June, 1972 List Price(USD): $11.95 |
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Title: Schaum's Outline of Set Theory and Related Topics by Seymour Lipschutz ISBN: 0070381593 Publisher: McGraw-Hill Trade Pub. Date: 01 July, 1998 List Price(USD): $16.95 |
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Title: Foundations of Mathematical Logic by Haskell B. Curry ISBN: 0486634620 Publisher: Dover Pubns Pub. Date: 01 June, 1977 List Price(USD): $15.95 |
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Title: Axiomatic Set Theory by Paul Bernays ISBN: 0486666379 Publisher: Dover Pubns Pub. Date: 01 February, 1991 List Price(USD): $12.95 |
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Title: Basic Set Theory by Azriel Levy ISBN: 0486420795 Publisher: Dover Pubns Pub. Date: 13 August, 2002 List Price(USD): $21.95 |
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