- Hardcover: 317 pages
- Publisher: Academic Press Inc; 2nd Revised edition edition (23 Jan 2001)
- Language English
- ISBN-10: 0122384520
- ISBN-13: 978-0122384523
- Product Dimensions: 16.5 x 1.9 x 23.5 cm
- Average Customer Review: 1.0 out of 5 stars See all reviews (1 customer review)
- Amazon Bestsellers Rank: 728,889 in Books (See Top 100 in Books)
- See Complete Table of Contents
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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
--This text refers to an alternate
Hardcover
edition.
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
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We assume that the reader already has some familiarity with normal everyday set-theoretic apparatus. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index
We assume that the reader already has some familiarity with normal everyday set-theoretic apparatus. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Customer Reviews
Most Helpful Customer Reviews
0 of 1 people found the following review helpful
Format:Hardcover
... 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 strong "desire" to fall apart, with the front pages almost ripped off and the next pages soon to follow... Academic Press/Elsevier should try to get a training in the UK on how to provide a decent structure for a book in that price range.
SECOND : impractical numbering of sections, theorems, subsections + no mention of sections at the top of the page, making the search difficult + a very dull layout ...
THIRD : A very peculiar way of proving theorems : quite a personal interpretation of induction and recursion (a way for Enderton to free himself from the burden of really getting at the bottom of things...). It seems like Enderton had enrolled in a marathonian effort to give tortuous proofs, often incomplete and based on fistulous definitions, which turn the reading into a continual second-guessing exercise, with its load of annotations...
Added to the annoying game of transferring part of the theory to a bunch of exercises.
FOURTH : Wiith a horrific set of notations, chapter 3 (on undecidability) is simply unreadable and I wish good luck to those who want to understand Gödel's theorems via such confused and confusing text...
FIFTH : I am perusing chapter 4 with the faint hope that it isn't a second-order magma...
I really wish that Peter Smith (his excellent "Introduction to Gödel's theorems", see my review) decide, one day, to write a book on mathemetical first- and second-order logic !!!
FIRST : As I reached half the book it was already giving signs of a strong "desire" to fall apart, with the front pages almost ripped off and the next pages soon to follow... Academic Press/Elsevier should try to get a training in the UK on how to provide a decent structure for a book in that price range.
SECOND : impractical numbering of sections, theorems, subsections + no mention of sections at the top of the page, making the search difficult + a very dull layout ...
THIRD : A very peculiar way of proving theorems : quite a personal interpretation of induction and recursion (a way for Enderton to free himself from the burden of really getting at the bottom of things...). It seems like Enderton had enrolled in a marathonian effort to give tortuous proofs, often incomplete and based on fistulous definitions, which turn the reading into a continual second-guessing exercise, with its load of annotations...
Added to the annoying game of transferring part of the theory to a bunch of exercises.
FOURTH : Wiith a horrific set of notations, chapter 3 (on undecidability) is simply unreadable and I wish good luck to those who want to understand Gödel's theorems via such confused and confusing text...
FIFTH : I am perusing chapter 4 with the faint hope that it isn't a second-order magma...
I really wish that Peter Smith (his excellent "Introduction to Gödel's theorems", see my review) decide, one day, to write a book on mathemetical first- and second-order logic !!!
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
16 reviews
53 of 57 people found the following review helpful
Still the best.
22 Sep 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 . . . .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
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
17 of 20 people found the following review helpful
Excellent Textbook with lots of examples
31 July 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.
5 of 5 people found the following review helpful
Best Intro. Logic Book Ever!
11 Sep 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.
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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