It helps that generally (ie unless you’re at Princeton/Cambridge/etc) the faculty at a given school will have come from much stronger schools than the grad students there, and similarly for undergrads/grads. And by “helps” I mean that it helps maintain the effect while explaining it, not that it helps the students any.
As far as the range of a recursive function goes, isn’t that the very definition of a recursive set?
I’m definitely enjoying Fixing Frege. This is the third Burgess book I’ve read (Computability & Logic and Philosophical Logic being the other two), and when it’s just him doing the writing, he’s definitely one of the clearest expositors of logic I’ve ever read.
Apparently, he also gets chalk all over his shirt when he lectures, but I’ve never seen this first-hand.