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Fundamentals of Mathematical Logic 1st Edition

by
Peter G. Hinman (Author)
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Peter G. Hinman (Author)
3.5 out of 5 stars 2 customer reviews
ISBN-13: 978-1568812625
ISBN-10: 1568812620
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Product Details

  • Hardcover: 896 pages
  • Publisher: A K Peters/CRC Press; 1 edition (November 15, 2005)
  • Language: English
  • ISBN-10: 1568812620
  • ISBN-13: 978-1568812625
  • Product Dimensions: 6.1 x 1.7 x 9.1 inches
  • Shipping Weight: 2.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,388,558 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

5.0 out of 5 starsA Comprehensive Graduate Text
By A Reader on July 25, 2007
Format: Hardcover Verified Purchase
If I were a young graduate student in mathematics looking for that one "perfect" graduate text on mathematical logic to purchase with my (very) limited income, I would buy a copy of Professor Hinman's book. In just under 900 pages, Hinman provides an extremely well written and informed introduction to propositional logic, first order mathematical logic, axiomatic set theory, model theory, and recursion theory. Indeed, the book is written so well that a motivated student with the requisite background can easily profit from independent study---a statement that simply cannot be made about many of the other "classic" references in this difficult field. One great virtue of having a single reference that introduces these diverse but interconnected areas is the uniformity of notation and definitions; the reader need not pull his hair out cross-referencing between texts that use wildly different notation and, occasionally, different definitions.

I studied mathematical logic at the University of Colorado--Boulder in the late 1970s. In those days, the logic students all depended on a standard list of references to prepare for the PhD qualifying examinations, and it is significant that all or nearly all of those works are still in print. At the introductory level we read the magnificent books on mathematical logic and set theory by Herbert Enderton. At the graduate level, we read Shoenfield, Monk, Mendelson, and Manin for mathematical logic, Chang and Keisler for Model Theory, Jech (and to a lesser extent, Kunen) for set theory, and Hartley Rogers for recursive function theory. In the course of plodding through these references, I discovered a wonderful comprehensive text by John Bell and Moshe Machover and quickly elevated it to primary status on my reading list.Read more ›
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2.0 out of 5 starsWhere's the proof?
By tecken on December 30, 2007
Format: Hardcover
Quoting the author Hinman (page xi): "A notable lacuna is Proof Theory,
which fails to appear largely due to the incompetence of the author in this area".
And he is correct: there is no proof theory in this book, no Hilbert axioms,
no Gentzen natural deduction nor sequent calculus, nothing (except for a cursory
13 page section out of 878).
So, on the one hand, we have the largest logic book I have ever seen
-- and yet, ironically, the most incomplete.
I'm sure there's a lot of good stuff in this book and it is written well but it's
missing half the story, i.e., it is missing an exposition of how one manipulates
symbols formally to prove theorems. Even the semantic, model-theoretic side is incomplete:
there's no semantic tableaux, no resolution. Also, at 878 pages, plausibly
a considerable portion is at an advanced level.
So, this is not a good introduction to logic.
By far the best introduction to logic I've found is "Mathematical Logic for
Computer Science" by Mordechai Ben-Ari. Serious/pure mathematicians of course will
want to continue with the likes of "An Introduction To Mathematical Logic"
by Elliott Mendelson.
7 Comments 17 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
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