Thanks for the helpful replies, everyone. FL Philip Scott wrote:
Dear Finn: as mentioned by Rosolini, you should definitely check out the book of Jaap von Oosten. More interesting from your point of view is to go to Jaap's webpage and look at the rather detailed criticism/ response of Jaap and Johnstone to a review by Peter Johnstone of Jaap's book. That probably has some things you're looking for. And, oc, Johnstone's still working on Elephant Vol.3 (who knows when it will appear) which may have some of this stuff.
There are unpublished notes by P. Freyd (I was at U.Penn on sabbatical in 1987 when he gave a course on this) on realizability topoi based on the allegories/ exact-completion method.
Phil Scott
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]