A Mathematical Introduction to Logic, Second Edition (Hardcover)

by Herbert B. Enderton (Author) "We assume that the reader already has some familiarity with normal everyday set-theoretic apparatus..." (more)
Key Phrases: sentential connective symbols, recursively axiomatizable theory, recursive partial function, Mathematical Introduction, Emil Post, Thoralf Skolem (more...)

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 -- Review

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

See all Editorial Reviews

Product Details

• Hardcover: 317 pages
• Publisher: Academic Press; 2 edition (December 2000)
• Language: English
• ISBN-10: 0122384520
• ISBN-13: 978-0122384523
• Product Dimensions: 9.3 x 6.5 x 0.7 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars See all reviews (10 customer reviews)
• Amazon.com Sales Rank: #567,466 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

42 of 45 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

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

15 of 16 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)

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 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. Only after equivalent material has been understood thoroughly can the more hardcore semantics and mathematics of Enderton's book be fully comprehended. And, gone at alone on one's free time such a progression might take up to 2.5 years, maybe more.

14 of 18 people found the following review helpful:

3.0 out of 5 stars Readable but a bit rough, July 11, 2005

By	Nathan Oakes (Ashland, Oregon) - See all my reviews

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 of thought, and exercises often require a significant conceptual leap from the preceding text. It was particularly annoying the way he suddenly switched to Polish notation for a while and then just as suddenly dropped it, without any obvious benefit. However, it is more accessible than most mathematical logic texts. The main competition for this text would be Ebbinghaus, which I prefer. The benefits of Enderton over that book are that it covers a wider range of topics and has a lot more exercises.