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Set Theory and Logic (Dover Books on Mathematics) Paperback – October 1, 1979

ISBN-13: 978-0486638294 ISBN-10: 0486638294 Edition: Reprint

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 496 pages
  • Publisher: Dover Publications; Reprint edition (October 1, 1979)
  • Language: English
  • ISBN-10: 0486638294
  • ISBN-13: 978-0486638294
  • Product Dimensions: 1 x 5.5 x 8.1 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #413,863 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

66 of 67 people found the following review helpful By A Customer on June 27, 2003
Format: 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.
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44 of 46 people found the following review helpful By galloamericanus on July 29, 2001
Format: 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.
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54 of 61 people found the following review helpful By A Customer on February 3, 1998
Format: 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.
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15 of 16 people found the following review helpful By JL on February 12, 2005
Format: Paperback
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.
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18 of 21 people found the following review helpful By Nathan Oakes on July 11, 2005
Format: Paperback
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.
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