A Friendly Introduction to Mathematical Logic

I purchased this book on behalf of a friend, so, I'm afraid I couldn't possibly make a personal comment. However, I'm told it served its purpose.

This is a good and clear introduction to first order logic. The authors have done their best to make the subject accessible, and the word "friendly" in the title is justified. However, there is no avoiding the fact that the subject is quite difficult. The main difficulty for most readers will be that many of the concepts are unfamiliar, and some of them are subtle. It is easy to get confused. I needed to read some chapters twice before I could make sense of the subject matter.Only a few of the proofs can be described as difficult. The majority are straightforward - but only if you have acquired a clear grasp of the concepts involved.The authors main goal is Godel's incompleteness theorems, and they approach the topic via two independent routes. The first is via logic proper, i.e. via an analysis of semantics and how statements in some formal language or other relate to a mathematical structure. The second route is via computable functions. Depending on how deep is your interest in mathematical logic, you could omit one or the other and still gain a lot from this book.

I have been trying to teach myself metalogic and mathematical logic from a standing start. This book isn’t for beginners like me, but it is nicely presented so I shall keep it as a reference book for comparison with others on the same subject, of which I would recommend Geoffrey Hunter’s Metalogic. One slight irritation is a joke at the beginning of the text about the immaculate conception. The author clearly doesn’t know what the immaculate conception is so he’d be better off trying to raise a laugh by sticking to things he knows about.