No, it's not up to date. (It's on my list of things to fix, but I don't have many spare cycles right now.) I'd start with a short set theory book (such as Naive Set Theory), follow it up with Computation and Logic (by Boolos), and then (or if those are too easy) drop me a PM for more suggestions. (Or read the first four chapters of Jaynes on Probability Theory and the first two chapters of Model Theory by Chang and Keisler.)

Edit: I have now updated the course list (or, rather, turned it into a research guide) that is fairly up-to-date (if unpolished) as of 6 Nov 14.