Re: Logical consequences of descent theory

In connnection with the descent theorem of Marek for pretoposes, the papers by Moerdijk and Vermeulen should be mentioned: Proper maps of toposes, Memoirs of the AMS, Vol 705 (2000). Proof of a conjecture of Pitts, Volume 143, Number 1 (1999), pp. 329-338 Descent theory has been a kind of definability theory from the beginning, I think. See, e.g., Andre Weil, The Field of Definition of a Variety, American Journal of Mathematics, Vol. 78, No. 3 (Jul., 1956), pp. 509-524. -wb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]