Preprint available

[categories <cat-dist@mta.ca>]

Date: Tue, 1 Jul 97 13:38 BST
From: Dr. P.T. Johnstone <P.T.Johnstone@pmms.cam.ac.uk>

The Pure Mathematics Department of Cambridge University has a new electronic
preprint server (accessible via our home page at http://www.pmms.cam.ac.uk).
The first preprint available may be of interest to people on the categories
mailing list: it is

C. Butz and P.T. Johnstone: Classifying toposes for first-order theories

Abstract: By a classifying topos for a first-order theory $\Bbb T$, we mean
a topos $\cal E$ such that, for any topos $\cal F$, models of $\Bbb T$ in
$\cal F$ correspond exactly to open geometric morphisms ${\cal F}
\rightarrow{\cal E}$. We show that not every (infinitary) first-order theory
has a classifying topos in this sense, but we characterize those which do by
an appropriate `smallness condition', and we show that every Grothendieck
topos arises as the classifying topos of such a theory. We also show that
every first-order theory has a conservative extension to one which possesses
a classifying topos, and we obtain a Heyting-valued completeness theorem for
infinitary first-order logic.

For those who would prefer to receive a hard copy of this paper, I shall be
bringing a supply with me to the Vancouver meeting.

Peter Johnstone