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よく一緒に購入されている商品
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Synopsis
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.
内容説明
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
* 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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カスタマーレビュー
最も参考になったカスタマーレビュー
16 人中、15人の方が、｢このレビューが参考になった｣と投票しています。
形式:ハードカバー
アメリカの数学科の１、２年生向けの授業でよく使われると言われる、定評ある
論理学の入門書です。もともと数学を知っている、あるいは数学的な思考に慣れ
た人向けに書かれていることもあり、取り扱いは数学的で厳密です。この厳密さ
は他の類書には見られないほどです。初めはとっつきにくいですが、慣れるとそ
の厳密さが気持ちよくなってきます。
論理学の入門書です。もともと数学を知っている、あるいは数学的な思考に慣れ
た人向けに書かれていることもあり、取り扱いは数学的で厳密です。この厳密さ
は他の類書には見られないほどです。初めはとっつきにくいですが、慣れるとそ
の厳密さが気持ちよくなってきます。
内容は一階命題論理、一階述語論理、モデル論の初歩、不完全性定理、二階述
語論理となっています。個人的に感銘を受けたのは述語論理のモデルと真理定義
の扱い、完全性定理、超準解析（最高！）、二階論理でした。
二階論理などはよい入門書が少ないこともあり、この本の取り扱いは貴重です。
ちょっと不満な点は、証明論に関して貧弱であることで、証明体系についてはほ
とんど学べません。そのことが一方で健全性や完全性の証明を容易にしているの
ですが、この点はモデル論を重視するアメリカの論理学教育の一端が見えるかな、
といったところです。
論理学を始めたごく最初の頃に読むのは、上級者の手助けがないときついでしょ
う。しかし、この本は初等論理学を学ぶ上での一つの到達点と言えると思います。
折に触れて読み返し、参考に出来る信頼の置ける本です。
29 人中、26人の方が、｢このレビューが参考になった｣と投票しています。
形式:ハードカバー
この本は、タイトルの通り、論理学を数学的に厳密に展開している。特に、他の本では（少なくとも僕の知る限り）数学的に厳密に展開されていないようなトピックがきちんと展開されている。ただし、その分はじめはすこし読むのが面倒かもしれないが、基礎的な事の理解にはいい本だと思う。又、（モデル等の）具体例が数学からのものが非常に多いけれども、基本的にはもし具体例がわからなければ飛ばしても、理解できるようになっているので安心して読める。この本のもう一つの大きな特徴は、命題論理は公理、推論規則といった体系を特に設定していないことだろう。だから、前半は命題論理といっても、その意味論の話に集中している。述語論理にしても、命題論理のトートロジーをプリミティブにとって体系関係を定義するのだが、このあたりは初めて見るとやや奇妙だが、それでも体系としての経済性から言えばいいやり方だと思う。というのも、いわゆる公理を用いる体系は、（メタ定理の扱いの点ではよいが）論理式の証明をするのに非常にわずらわしい事が多い。そこらへんが緩和されているわけです。記述は簡潔だが、丁寧。ついている問題は、ものによっては難しいけれども、大体のものはいい問題だと思う。ちなみに、述語論理の完全性定理についてはこの本の評価は非常に高い。不完全性定理の証明も書いてある。そんなわけでお勧めです。
Amazon.com で最も参考になったカスタマーレビュー (beta)
Amazon.com:
16件のカスタマーレビュー
57 人中、53人の方が、｢このレビューが参考になった｣と投票しています。
Still the best.
2003/9/22
形式:ハードカバー
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
20 人中、17人の方が、｢このレビューが参考になった｣と投票しています。
Excellent Textbook with lots of examples
2002/8/1
形式:ハードカバー
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 人中、5人の方が、｢このレビューが参考になった｣と投票しています。
Best Intro. Logic Book Ever!
2010/9/11
形式:ハードカバー
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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