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Mathematical Logic (Dover Books on Mathematics) Paperback – December 18, 2002

ISBN-13: 978-0486425337 ISBN-10: 0486425339

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 432 pages
  • Publisher: Dover Publications (December 18, 2002)
  • Language: English
  • ISBN-10: 0486425339
  • ISBN-13: 978-0486425337
  • Product Dimensions: 5.5 x 0.9 x 8.5 inches
  • Shipping Weight: 12.8 ounces
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #106,559 in Books (See Top 100 in Books)

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Customer Reviews

4.3 out of 5 stars
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20%
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See all 10 customer reviews
I like this kind of stuff.
Myrna B. Tagayun
The book is comprehensive and more sophisticated and detailed than I needed, but you can't blame the book for that.
G. Michael Zeno Jr.
D. Goldrei's "Propositional and Predicate calculus" 3.
André Gargoura

Most Helpful Customer Reviews

27 of 29 people found the following review helpful By Trenton F. Schirmer on July 16, 2008
Format: Paperback Verified Purchase
This book was written by one of the great American mathematical minds of this century. I've read it cover to cover and it happens to be my favorite logic book for its scope, depth, and clarity. Kleene uses a combined model-theoretic and proof-theoretic approach, and derives many interesting results relating the two (he also gives mention to special axioms for Intuitionistic logic). Although his focus in the first part of the book is on a more or less mathematical treatment of standard first-order predicate logic (augmented later by functions and equality), he also spends considerable time discussing the ways in which formal logic can and should be used to analyze "ordinary language" statements and arguments. After setting the groundwork, he moves onto subjects such as set theory, formal axiomatic theories, turing machines and recursiveness, Godel's incompleteness theorem, Godel's completeness theorem, and just about every interesting subject relating to logic in the first half of the twentieth century.

For the mathematically inclined self-teacher, Kleene's exposition should not be difficult at all, in fact I found it remarkably clear compared to other mathematical treatments of the subject (which are necessary if one wants to understand the deeper results). I suppose less mathematically inclined readers could try Irving Copi's "Symbolic Logic" as a start, although even that requires some mathematical proficiency, and since it doesn't cover many of the things you will want to know about, you'll end up coming back to a book like Kleene's anyway. So to summarize, if you want to learn the hard stuff (from the first half of the twentieth century--which includes just about everything the layman/philosopher wants to know), there is no better or easier way.
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6 of 6 people found the following review helpful By Joel Zela Casaverde on November 22, 2011
Format: Paperback Verified Purchase
I bought this book based on the short altough extremely positive review in the bibliography section of Hofstadter's GEB. And it has proven to be one of the my best acquisitions. The books is wonderfully written, very detailed indeed, so it makes it easy to follow the proofs. It comes along with exercises at the end of every paragraph (chapters are divided into paragraphs) so you can process and reinforce what has been learned.
I have worked with plenty of logic books (among them: Suppes', Gamut's, Machover's, etc) but I am loyal to Kleene's.
What it attracks me the most is that it not only contains detailed and rigorous proofs of the most important theorems of logic, but that it also comes with philosophical considerations of one of the best logician's of the 20th century. There are other parts too where Kleene includes a piece of history, for instance, about the Löwenheim-Skolem theorem: delightful.
Buy it 'cause you won't regret it.
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60 of 79 people found the following review helpful By Christopher Schroen on July 19, 2004
Format: Paperback
Ten years ago, I took an undergraduate course in symbolic logic. Wishing recently to refresh my (extremely rusty) memories of the propositional calculus and the first-order predicate calculus, I picked up this meaty text and was extremely dismayed to find myself soundly defeated within the first few pages. Kleene does not even make a pretense of holding the reader's hand: either you get it or you don't. There is nothing even remotely "user-friendly" about this book's presentation of its material.
If one were to read this book under the guidance of a teacher, I think it might be worthwhile. It may not be fair for me to blame the author for my inability to understand his writing. If you're smarter than I am, you might breeze right through it.
I cannot recommend this book, though, good though it may be, for anyone who wishes to teach him/herself logic, nor for anyone who wishes to brush up on the subject. There are exercises for the reader to test his/her understanding of the material, but no answer key is provided. This is heavy-duty stuff, and not well-suited to the self-teacher.
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11 of 13 people found the following review helpful By Independent Studyer on May 25, 2011
Format: Paperback Verified Purchase
My problem with Kleene's Mathematical Logic is simply that its layout is terrible. There is hardly any white space in the text, so the entire book reads like a giant run-on sentence. This makes it difficult to find information that you want when you want to refer to a previous topic. There is also no glossary (defined terms are italicized in otherwise normal sentences, and hardly stand out at all. I generally highlighted them, since that was my only hope for referring to them later, short of typing my own glossary). There is also no answer key, which in my opinion is an extremely important element of any textbook.

That being said, all of the information that you could want is there. Simple concepts are built up appropriately before more abstract ones are given. Proofs of all important theorems are provided. Examples and exercises are abundant. In order to motivate you, the author simply insults your intelligence every once and a while, and you are thus determined to prove him wrong (I actually did enjoy this aspect of Kleene's style).

In summary - If you are determined, you can teach yourself mathematical logic from this book. However, you can make this undertaking much easier on yourself by getting a more readable textbook.
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7 of 8 people found the following review helpful By André Gargoura on November 7, 2012
Format: Paperback
I would not add much by saying that "Introduction to MetaMathematics" (IM) remains a masterpiece, even though the style is a bit oldish...

On the the other hand, "Mathematical Logic" (ML) brings a definite plus, but is by no means a replacement, rather a necessary complement.

As I planned to study both, the problem posed was the order in which one should approach those books : Historically ? By increasing or decreasing difficulty ? In parallel, in order to see how Kleene's ideas -- and the field -- have evolved between 1952 and 1966, and subject by subject ?

I chose the third an most difficult path... And the journey was a thrill !

Here is how I planned this strange exploration : IM, ch. 1 to 7 ; ML, ch. 1 to 4 ; IM, ch. 8 ; IM, Part III ; ML, ch. 5 : IM, ch. 14 ; ML, ch. 6 ; IM, ch. 15.

ML is certainly less difficult but contains a fair amount of footnotes linking it to IM, i.e. studying IM is simply inevitable and enjoyable, even though some parts are really tough and must be "examined in a cursory manner", as suggested by Kleene, e.g. ch. 14 & 15.

IM, part III, is a thorough treatment of recursive functions, the best in my opinion and is not part of ML.

All in all, the two together rank very high in logic books, perhaps highest.

This book now stands in my list of outstanding books on logic :

1. A. Tarski's "Introduction to Logic", a jewel, followed by P. Smith's superb entry-point "An introduction to Formal logic" and the lovely "Logic, a very short introduction" by Graham Priest

2. D. Goldrei's "Propositional and Predicate calculus"

3. Wilfrid Hodges' "Logic", followed by Smullyan's "First-order logic".

4. P. Smith's "An introduction to Gödel's theorems".
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