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A Mathematical Introduction to Logic, Second Edition Hardcover – January 5, 2001

ISBN-13: 978-0122384523 ISBN-10: 0122384520 Edition: 2nd

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Product Details

  • Hardcover: 317 pages
  • Publisher: Academic Press; 2 edition (January 5, 2001)
  • Language: English
  • ISBN-10: 0122384520
  • ISBN-13: 978-0122384523
  • Product Dimensions: 6.1 x 0.8 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.4 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #249,706 in Books (See Top 100 in Books)

Editorial Reviews

Review

Reasons for This Book's Success
"Rigor, integrity and coherence of overall purpose, introducing students to the practice of logic . . ."
--Douglas Cannon, University of Washington
"The book is clearly and carefully written. I adopted this text because of its detailed and rigorous treatment of the predicate calculus, detailed and optimal treatment of the incompleteness phenomena, standard notation as developed by the Berkeley school."
--Karel Prikry, University of Minnesota
"It is mathematically rigorous [and] it has more examples than other books . . . I definitely would use a new edition of this book."
--Sun-Joo Chin, University of Notre Dame

From the Back Cover

About this book
An accessible, flexible introduction to the subject of mathematical logic, the second edition of this popular and widely-adopted text has been revised to be appropriate for courses enrolling either advanced undergraduates or graduate students.
Like the First Edition, this book is an introduction to the concepts of proof, truth, and computability. This Second Edition has additional examples and explanations to help the reader. Footnotes indicate optional paths through the material that the user might wish to take. Topics relevant to computer science, such as finite models, are also now included.
Reasons for This Book's Success
"Rigor, integrity and coherence of overall purpose, introducing students to the practice of logic . . ."
--Douglas Cannon, University of Washington
"The book is clearly and carefully written. I adopted this text because of its detailed and rigorous treatment of the predicate calculus, detailed and optimal treatment of the incompleteness phenomena, standard notation as developed by the Berkeley school."
--Karel Prikry, University of Minnesota
"It is mathematically rigorous [and] it has more examples than other books . . . I definitely would use a new edition of this book."
--Sun-Joo Chin, University of Notre Dame

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Customer Reviews

Proofs are not in depth and the examples BARELY help.
IdahoPotato
While he does make mention of some algebraic stuff in passing, I would say you don't really need any specific prerequisites to read this.
Christian
It's the only MATH book on logic out there that is easy to understand and yet formal enough to be considered "mathematical."
A Customer 2000

Most Helpful Customer Reviews

58 of 63 people found the following review helpful By Jason T on September 21, 2003
Format: Hardcover
I review the classic FIRST EDITION. If you buy only one book on mathematical logic, get this one. It's by far the best logic book (see my other reviews) that is both 1)introductory and 2)sufficiently broad in scope and complete. The exposition is very clear and succinct- its suitable for beginners without getting wordy. Enderton always clearly explains what he's doing and why, keeping the reader focused on the big picture while going through the details. He helps to place topics in perspective, and has organized the book so readers can skip some of the more involved proofs and sections on the first reading.

Besides being easy to learn from, it's also the most rigorous introductory book I've seen- a rare combination. The proofs are detailed and complete, instead of the usual hand-waving or leaving everything as an exercise for the reader. There are some weak points in it, but overall you're not going to find a better book. It requires a little more 'mathematical sophistication' than most intro books- but if you've had some logic in a computer science course, or a little combinatorics or abstract algebra you'll be more than ready. Familiarity with automata/computability theory will help you in a few of the sections. Although Enderton is very good, it always helps to get several books on a subject- I'd recommend you pick up cheap copies of Boolos & Jeffrey's _Computability and Logic_ and Smullyan's _First-order logic_ as supplements.

Here is the complete table of contents for the first edition, c1972:

Chapter Zero - USEFUL FACTS ABOUT SETS . . . .
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15 of 15 people found the following review helpful By Eric "Siggy" Scott on May 8, 2012
Format: Hardcover Verified Purchase
There are two types of mathematical texts: source code (definition-theorem-proof-remark-definition-...), and books intended to educate via explanations of where we came from, where we're going, and why we should care. Enderton's (2nd edition) text is an actual *book,* albeit not a superb one (compare to Simpson's free text on Mathematical Logic at [...], which fits my definition of "source code"). For this he automatically earns 2 stars -- though in any field except mathematics, this would earn him nothing.

The prose itself is easy to follow, and makes suitable use of cross-references -- you will not find yourself stumped for 30 minutes trying to substantiate a casual statement made half-way through the book, as with some mathematical authors. High-minded ideas such as effectiveness and decidability appear (briefly) at the end of chapter one, so you don't have to read 180 pages before any "cool" things are presented, and there are occasional (but too few) sentences explaining what the goal of a formalism is before it is developed. Chapter 1, which covers sentential (propositional) logic, also has a short section on applications to circuit design, providing some much-welcome motivation for the material. Model theory is also integrated with the discussion of first-order logic in chapter 2, which is preferable to having it relegated to a later section as in some texts. The book also gives heavy emphasis to computational topics, and even gets into second-order logic in the final chapter -- a very complete coverage for such a small introductory text. These virtues combine to earn it a third star.

My primary complaint is the manner in which rigor is emphasized in the text to the neglect (rather than supplement) of a coherent big picture -- losing two full stars.
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19 of 23 people found the following review helpful By M. Vishnu on July 31, 2002
Format: Hardcover
I used this book for self study of Mathematical Logic with the aim of understanding Godel's incompleteness theorem. I also referred to other introductory Mathematical Logic books. In my opinion, this book is by far the best among them. Very readable and contains lots of carefully selected examples.
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9 of 10 people found the following review helpful By A Customer 2000 on September 11, 2010
Format: Hardcover
This is easily the BEST intro. logic book every written. (Yes, I sound horribly biased.) This books covers everything from Sentential Logic to 1st Order to Recursion to a bit of 2nd Order Logic. It's the only MATH book on logic out there that is easy to understand and yet formal enough to be considered "mathematical." Even the treatment of Sentential Calc. brings interesting tidbits (ternary connectives, completeness, compactness, etc). Truth and models (the heart of it) are treated incredibly clearly. Extra topics such as interpretations between theories and nonstandard analysis keep things exciting (for a math book). His treatment of undecidability is well-written and lucid. The second order stuff is fun.

I loved this book. As far as math teachers go, Enderton is top notch. Even someone as unacquainted with math as I was when I studied the book (and as I still am now, I guess) understood what was going on. To be honest though, I did have one advantage, I was a student of the master, Enderton, himself. I learned so much about logic (and math in general) from this great book. I was fortunate enough to study some more with Enderton throughout my years as a student. Of course, I went through his "Elements of Set Theory" which is also fantastic. Too bad he never wrote a book on model theory...But, you never know; maybe someday he will.
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