Date: Thu, 2 May 1996 23:37:03 -0300 (ADT)
Subject: coherent toposes 

Date: Thu, 2 May 1996 15:03:07 +0200 (MET DST)
From: Paul Johnson <johnson@math.muni.cz>

In all the resources I have available,
Deligne's Theorem (axiom) is proven to
be a consequence of axiom of choice.
(That is, in TTT, Johnstone's Topos Theory, 
Maclane/Moerdijk).
Am I wrong to think it is actually a consequence
of only prime ideal theorem???
The best possible result I can imagine is that
***constructively***
every coherent topos E admits a surjection
sh(X) ---> E (ie epimorphism in the category of
geometric morphisms) where X is a coherent locale.
But I can't prove it. Paul.