Logic for Mathematicians

"Logic for Mathematicians" starts well, giving clear and formal explanations of formal logical systems and the predicate calculus. There are plenty of examples in the book, many of which clarified difficult or poorly worded definitions. I have been using this book recently to help me understand concepts that are much more tersely introduced in Elliott Mendelson's "Introduction to Mathematical Logic". This latter book may be better for it's later proofs (e.g., Godel's incompleteness theorem), but the early explanations of how the formal systems work is more easily understood from "Logic for Mathematicians". I gave it only four stars, though, because it becomes a bit less readable later on.The proof of Godel's theorem is incomplete; instead, the author uses convincing examples to demonstrate the generality of recursive functions and from there shows Godel's results.