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A Mathematical Introduction to Logic, Second Edition [Hardcover]

Herbert Enderton (Author), Herbert B. Enderton (Author)
3.4 out of 5 stars  See all reviews (16 customer reviews) |
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Book Description

Publication Date: January 5, 2001 | ISBN-10: 0122384520 | ISBN-13: 978-0122384523 | Edition: 2
A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses.
* Reduced mathematical rigour to fit the needs of undergraduate students

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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

Product Details

  • Hardcover: 317 pages
  • Publisher: Academic Press; 2 edition (January 5, 2001)
  • Language: English
  • ISBN-10: 0122384520
  • ISBN-13: 978-0122384523
  • Product Dimensions: 9.5 x 6.5 x 0.7 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.4 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #512,222 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
53 of 57 people found the following review helpful
Still the best. September 21, 2003
By Jason T
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 . . . .1
Chapter One - SENTENTIAL LOGIC/ Informal Remarks on Formal Languages 14 /The Language of Sentential Logic 17/ Induction and Recursion 22/ Truth Assignments 30/ Unique Readability 39/ Sentential Connectives 44/ Switching Circuits 53/ Compactness and Effectiveness 58

Chapter Two - FIRST-ORDER LOGIC/ Preliminary Remarks 65/ First-Order Languages 67/ Truth and Models 79/ Unique Readability 97/ A Deductive Calculus 101/ Soundness and Completeness Theorems 124/ Models of Theories 140/ Interpretations between Theories 154/ Nonstandard Analysis 164

Chapter Three - UNDECIDABILITY/ Number Theory 174/ Natural Numbers with Successor 178/ Other Reducts of Number Theory 184/ A Subtheory of Number Theory 193/ Arithmetization of Syntax 217/ Incompleteness and Undecidability 227/ Applications to Set Theory 239/ Representing Exponentiation 245/ Recursive Functions 251

Chapter Four - SECOND-ORDER LOGIC/ Second-Order Languages 268/ Skolem Functions 274/ Many-Sorted Logic 277/ General Structures 281
Index 291
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17 of 20 people found the following review helpful
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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5 of 5 people found the following review helpful
Best Intro. Logic Book Ever! 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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Most Recent Customer Reviews
Quite readable, but misses the forest in favor of trees
There are two types of mathematical texts: source code (definition-theorem-proof-remark-definition-... Read more
Published 8 days ago by Eric "Siggy" Scott
Difficult to Follow
I had to buy this book for one of my classes. It's terrible! I thought abstract algebra was hard to follow but this book makes abstract algebra seem like a cakewalk. Read more
Published 2 months ago by IdahoPotato
Great Book, Horrible Binding
This is a great book as far as content goes. I would give the book five stars if it wasn't for the poor binding these books seem to have. Read more
Published 4 months ago by Rob S
Neither "great", nor "the best" and even less "terrific"...
... contrary to what I read among the wealth of dithyrambic adjectives concerning that book !!!

FIRST : As I reached half the book it was already giving signs of a... Read more
Published 4 months ago by Gargoura
The quality of this version of the book was awful.
My problem is with the quality, not the contents. Through the first chapter, I actually quite liked the author's delivery of the material. Read more
Published 7 months ago by Collin
NOT A GOOD CHOICE FOR THE BUKKAKE LOVER
The title says it all. If you are one of the chosen few, you are better off buying a different logic book.
Published on November 15, 2009 by A. Isbell
Fascinating material, poor proofs
Maybe it's because I'm only in undergrad, but I found a lot of the proofs in this book to be incomplete and hard to penetrate. Read more
Published on July 18, 2009 by †
From the point of a CS student
It's very hard to review a book like this without letting personal interest in the subject bias you... but I'll try ;).

I used this book in my fourth year at Berkeley. Read more
Published on September 5, 2008 by Daniel Wong
John Wilson
Keen students may find if they study and parse both editions of Enderton's

Logic they may find much of interest. Read more
Published on July 24, 2007 by Martin O'riordan
Readable but a bit rough
It tries to be a readable undergrad introduction and mostly succeeds. Explanations are generally not tight and memorable, proofs seem loose, there are sometimes gaps in the train... Read more
Published on July 11, 2005 by Nathan Oakes
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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We assume that the reader already has some familiarity with normal everyday set-theoretic apparatus. Read the first page
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sentential connective symbols, recursively axiomatizable theory, recursive partial function, enumerability theorem, computability approach, numbered language, enumerable iff, strong undecidability, sentence symbols, enumerable relations, induction postulate, deductive calculus, sentential logic, decidable set, axiom group, representable functions, recursive iff, prenex formula, countable language, admits elimination, proper initial segment, prime formulas, new constant symbols, countable structure, compactness theorem
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Mathematical Introduction, Emil Post, Thoralf Skolem
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