First model theory seminar today. We were just limbering up reading the first chapter and a bit into the second chapter. It fell to me to try to say something to introduce the reading — difficult as nothing very exciting is going on yet: the interesting stuff starts next week. So I offered a few arm-waving thoughts about the way Hodges defines ‘structure’ and about his (and other model theorist’s) stretched use of ‘language’. Here is what I said.
[Later: In the light of comments, I’ve slightly revised the intro piece to make what I was saying clearer at a few points. And of course, I was struggling a bit to find anything thought-provoking to say about the very introductory opening pages of Hodges’s book! — so I’m no doubt slightly over-stating the points too.]