Hm. Sorry for attempting to hijack the thread, but I have a related question. I'm enrolled in a Mathematical Logic & Computability course this semester, which has the goal of covering up to Godel's Incompleteness theorems. Here's the course description
"The basic metatheorems of first order logic: soundness, completeness, compactness, Lowenheim-Skolem theorem, undecidability of first order logic, Godel's incompleteness theorem. Enumerability, diagonalization, formal systems, standard and nonstandard models, Godel numberings, Turing machines, recursive functions, and evidence for Church's thesis. (Same course as PHIL 4003*)"
I've had no formal previous courses in Logic (such as Symbolic Logic), but as a pure math major I've learned much of it through many proof based math courses.
Think I'm over my head? If anyone's familiar with the text, we're using Enderton's Mathematical Introduction to Logic, second edition