A Mathematical Introduction to Logic

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.

Enderton's writing is the best I've seen in any introductory math textbook; he is lucid, well organised, comfortably paced but free of expository flab. The exercises (judging from chapters 2 and 3) are not terribly difficult, but quite useful in building one's intuition and connecting logic to other mathematics. I had the book for my Logic class as a first-semester sophomore with very little experience with proofs and no abstract algebra, and found it quite accessible. I guess the book starts off with an advantage, being about a subject as interesting as logic, but that does not seriously detract from its merit.

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.

One of the very best introductions to logic, combining readability and depth. An excellent book.

This is a great introductory book. Some set theory, sentential logic, first-order logic, metatheory/model theory,number theory, undecidability and Godel's Incompleteness, and Second-Order Logic. You still have to take a lot of time trying to soak in the stuff, but that's because of the complex nature of the material, not the book. The book itself is really good.