A Mathematical Introduction to Logic, Second Edition [Hardcover]

Herbert Enderton (Author), Herbert B. Enderton (Author)

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

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: 9.3 x 6.2 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #163,055 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

52 of 56 people found the following review helpful:

4.0 out of 5 stars Still the best., September 21, 2003

By 

Jason T (Canada) - See all my reviews

This review is from: A Mathematical Introduction to Logic, Second Edition (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

30 of 33 people found the following review helpful:

5.0 out of 5 stars Moderately difficult and very effective, July 18, 2006

By 

J. Jeremy Meyers (Stanford, CA) - See all my reviews
(REAL NAME)   

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This review is from: A Mathematical Introduction to Logic, Second Edition (Hardcover)

This is the most clear book on intermediate level logic that is available. I have many of the logic books that are on its level, and this one is perfect. It covers the most important, difficult concepts in the easiest way possible. It is above all clear (though very terse). It is easier than Mendelson's quasi-research-problem text but, in my opinion, as it pertains to First Order Logic and Computability Theory, one learns no more through Mendelson's approach.

Perhaps its only problem is that it might be just a bit too difficult without an understanding, helpful instructor (or TA) to guide one through the exercises. At any rate an effective progression up to the book might entail: Patty's "Foundations of Higher Mathematics", to Klenk's "Understanding Symbolic Logic", to "Logic, Sets, and Recursion" by Causey. Well, perhaps one might get by with just "Language, Proof, and Logic" by Barwise and Etchemendy. Nonetheless, only after equivalent material has been understood thoroughly can the more mathematical nature of Enderton's book be fully comprehended. And gone at alone on one's free time, such a progression will probably take 2 years, but maybe more.

17 of 20 people found the following review helpful:

5.0 out of 5 stars Excellent Textbook with lots of examples, July 31, 2002

By 

M. Vishnu (Petaluma, California United States) - See all my reviews

This review is from: A Mathematical Introduction to Logic, Second Edition (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.