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A Course In Mathematical Logic

3 customer reviews
ISBN-13: 978-0720428445
ISBN-10: 0720428440
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Editorial Reviews


The book is valuable for anyone interested in mathematical logic and may serve as a reference source for graduate students and specialists.
Zentralblatt für Mathematik

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Product Details

  • Hardcover: 620 pages
  • Publisher: North Holland (January 15, 1977)
  • Language: English
  • ISBN-10: 0720428440
  • ISBN-13: 978-0720428445
  • Product Dimensions: 6.1 x 1.3 x 9.2 inches
  • Shipping Weight: 2.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #2,416,600 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

25 of 25 people found the following review helpful By Paul Corazza on August 14, 2001
Format: Hardcover
When I was in my third year of graduate school and was deciding to specialize in set theory, I realized that it was time to get some formal training in first-order logic and model theory. At our school, there were no courses in foundations at all, so I had to find the right book and map out a course of study for myself. I sat in on a seminar for more advanced students that was going through Chang and Keisler (model theory); although I now use this as a basic reference, at the time I needed a more systematic treatment of first-order logic before getting into the details of model theory.
One day I discovered this book by Bell and Machover. It was exactly what I needed. The first three chapters are just what you need to get a solid grounding in first-order logic, covering the soundness, completeness and compactness theorems.
As I was working through the book, I noticed that the incompleteness theorems weren't treated till the 7th chapter -- this, along with the fact that the exercises were so much fun kept me pushing forward one chapter at a time.
Chapter 4 deals with Boolean algebras. I'd alreday had quite a bit of general topology before starting this chapter, so when the duality between Boolean algebras and Stone spaces is explored in some detail in the exercises, it was really a blast. A lot of material is covered in this chapter; the authors never tell you that they chose just the material you will need if you go on to study the Boolean algebra approach to forcing. (They actually give you a taste of Boolean-valued models in Chapter 5, but that's it for forcing in this book; however, the first author, Bell, wrote another book called Boolean-Valued Models and Independence Proofs in Set Theory that provides the most complete treatment of the subject available in book form.
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19 of 19 people found the following review helpful By Farogh Dovlatshahi on May 29, 1999
Format: Hardcover
This is probably one of the most oustanding textbooks on advanced mathematical logic written this side of the century.
But, it is surprising to me how difficult it is to find it in any libarary in USA. Even more surprising, however, is that, after all these years, it is not available at an affordable price. (It would be hasty to suggest that some publishers are motivated by greed than a desire to inform and educate, I am sure there are better reasons -- with the reservations that go with saying this, of course.).
On the cheerful side, I had the good fortune to sit on most of this course given by Moshe Machover in London. He is an outstanding logician and teacher. As a human being he is profound and just. He used to say, with a humorous matter-of-factness, something to the effect that he hoped we were not filled with "malaise" his favourite word.
The coverage is thorough and deep. The book is sufficiently advanced for it to be used as a textbook for a Master Level Introduction in Logic. It was being used in this way at London University (in 1979).
Thus it takes you further than most logic books that seek to teach the same set of topics. After covering early theorems in, say, model theory, it goes on to prove advanced theorems well beyond the standard texts on logic. The book, as I mentioned prepares you, relative to the British system, for an MA degree -- and so perhaps, a pre-amble to MPhil and, presuemeably, PhD levels.
You might need to augment this book with some other books in Topology, to follow some of the topological theorems).
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13 of 15 people found the following review helpful By Nathan Oakes on July 11, 2005
Format: Hardcover
Bell & Machover is meant for a one-year graduate course and is comparable to the more well-known text by Shoenfield. B&M is larger than Shoenfield, having additional chapters on Boolean algebra, intuitionist logic, and nonstandard analysis. There are a few newer things in B&M and they use the tableau method, which Shoenfield doesn't. Otherwise, they have about the same coverage, trading off as to which has more detail on this or that item. The main difference is in the writing style. The delivery in B&M is less articulate, proofs are terse and schematic, and problems have little setup. I find it harder to follow the train of thought in B&M than in Shoenfield and would not want to try learning anything for the first time from it.
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