Homomorphisms as "structure-preserving" maps

Landau

Yes.
The precise statement is that [tex]\textbf{Toph}[/tex] is not concretizable, meaning there does not exist a faithful functor [tex]F:\textbf{Toph}\to\textbf{Set}[/tex]. A proof of this statement can be found here.

Fredrik

Sorry, I didn't see the question until now. I first read about first-order formal languages, "structures" and what it means for a set of sentences to "logically imply" another sentence, in Enderton, and in Rautenberg. I don't think either of them is really easy to follow, so it was really helpful to have access to both. Then I bought Kunen's book "Foundations of mathematics". That's a very good book, so I can recommend it without reservations. But I got the feeling that a lot of the stuff that I found easy to understand would have been quite hard to understand if I hadn't read the about the stuff I mentioned above in Enderton/Rautenberg first.