It's a philosophy course at my uni, not a math course. The math version of the course is only offered in the fall.
We cover Compactness (which I'm pretty familiar with already), the Lowenheim-Skolem theorems, Godel's Incompleteness Theorems (which I'm also familiar with), as well as mathematical and theory of mind related implications of the incompleteness theorems.
I can't seem to find a copy of your book online...