I know very basic model theory (compactness, Lowenheim-Skolem, EF games, at that level), and I'd like to pick up more, mostly out of intrinsic interest and partially because I think it would give me an interesting perspective as I dive into my main subject, which is algebraic geometry.
I've been told that the best source for this sort of thing is Marker. After flipping through it I'm kind of confused about how connections between the subjects arise. Are the applications of model theory to algebraic geometry strictly classical? Are nonclassical applications too advanced to show up in something like Marker?
I ask because there's no mention at all of sheaves in Marker and nothing really about categories, and from a little googling this doesn't seem to be unusual. I'm not one to demand categorification for no reason but these are how the basic objects of modern a.g. are defined so I would expect them to show up in applications from a closely linked subject.