I put some quick notes together for myself for the Hodges reading group yesterday: I’ll work away at them again in the next few days (and certainly before the next seminar), and post the resulting after-the-event handout here, for it’s worth [Later, this might take longer than I wanted]. I must say that the Hodges book is turning out to be harder going than I had imagined: he is capable elsewhere of writing about difficult stuff with verve and great clarity, but here things get a lot denser. I thought it might just be that my pure maths (group theory and the like) is rusty enough for me not to be getting enough out of some of the examples he gives: but then some mathmos have expressed similar views about his approachability.
A very noticeable difference in style is emerging between a logic reading group run for philosophers and one with a mixed group of philosophers, mathmos and compscis. Philosophers — ok, our friendly local lot — seem to be happy to share their ignorance, and take turns week-by-week to introduce a chapter or a paper, albeit fairly briefly, even if they make no pretence to really be on top of the stuff. And they will dive into the discussion, cheerfully asking for clarification, or trying out toy mini-examples, etc. Mathmos and compscis on the other hand — although personally a perfectly friendly bunch! — seem on the whole very reluctant to volunteer to have a bash at introducing a chapter, or indeed to say anything much after someone has given the intro. Which is a pity, as I learn a lot from the exchanges when they do happen.
I wonder whether some of the density is due to the shortening. A quick comparison on one part – re imaginary elements – left me unsure. Once he reached the point where imaginaries were defined, the text was pretty much the same in both books; but I thought the way the longer book got to that point was more interesting to read.
I also wonder whether all (current) model theory texts at that level will have a similar problem, or whether some (Chang and Keisler maybe? Poizat?) would be more approachable.
BTW, if Amazon is correct, the longer book will be appearing in paperback later this year, priced 50 pounds, which is a lot though, unfortunately, not out of line with prices for many other maths and logic texts. :( At least it’s less than half the absurd hardcover price.
Also BTW, re the project of explaining forcing, Hodge’s book Building Models by Games might be included.