Set Theory and Logic

by Robert Roth Stoll

Book Overview

Set Theory and Logic is the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. One of the most complex and essential of modern mathematical innovations, the theory of sets (crucial to quantum...

• Format: Paperback
• Language: English
• ISBN: 0486638294
• ISBN13: 9780486638294
• Release Date: October 1979
• Publisher: Dover Publications
• Length: 512 Pages
• Weight: 1.20 lbs.
• Dimensions: 1.0" x 5.6" x 8.2"

Customer Reviews

Incredible Best Buy

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 topicis 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 approachZF 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.

Unusually clear treatment of very abstract matters.

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.

Good book that falls short of being a great book.

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.