Any suggestions for a course in Mathematical Logic? I am teaching a topics course for Mathematics majors (at Temple), and am considering Logic as the topic. I was wondering if people (a) have suggestions for an appropriate text and (b) how much might be reasonable to cover in a semester. Is it feasible to end with a little model theory, or would that be a pipe dream?
EDIT
The students are theoretically math majors, and the title of the course is "Senior Problem Solving", so they are seniors with high probability. Which means that they have a couple of courses in real analysis, and one in abstract algebra.
 A: Kenneth Kunen recently wrote a wonderful introduction to Mathematical Logic, called "The Foundations of Mathematics" (ISBN:  978-1-904987-14-7), published in 2009.  The book's only prerequisite is the mathematical maturity that an Introduction to Analysis course would provide, so it sounds like your students would be prepared.  The book provides a brief introduction to axiomatic set theory, model theory, and computability theory; and it culminates with a proof of Godel's incompleteness theorems and Tarski's theorem on the non-definability of truth.  There are also a couple brief discussions of the philosophy of mathematics; these are given from the perspective of the working mathematician, and they are used to motivate the material.  And they are very helpful.  In fact, the most salient thing about this book is that it is exceptionally clear, well-written, and easy to learn from.  (Kunen also wrote "Set Theory:  An Introduction To Independence Proofs" which is also exceptionally clear, well-written, and easy to learn from).  Your students will be grateful for the fact that this book is available (new) on amazon.com for less than $25.
A: I think it is very doable.  I took a class like that as an undergrad.  The textbook was Enderton's "Introduction to Mathematical Logic".  It did enough Hilbert-style proof theory to get up to the incompleteness theorem, then discussed models, interpretations, Tarski's definition of truth, etc.  It seemed great at the time and wasn't a terribly hard course.  My gripe these many years later is that I wish it had said something about sequent calculus since that would have changed how I thought of logic if I'd known about it at the time.
