TY - JOUR
AU - Carsten Butz
AU - Peter Johnstone
PY - 1997/01/20
Y2 - 2020/02/20
TI - Classifying Toposes for First Order Theories
JF - BRICS Report Series
JA - BRICS
VL - 4
IS - 20
SE - Articles
DO - 10.7146/brics.v4i20.18946
UR - https://tidsskrift.dk/brics/article/view/18946
AB - By a classifying topos for a first-order theory T, we mean a toposE such that, for any topos F, models of T in F correspond exactly toopen geometric morphisms F ! E. We show that not every (infinitary)first-order theory has a classifying topos in this sense, but wecharacterize those which do by an appropriate `smallness condition',and we show that every Grothendieck topos arises as the classifyingtopos 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.
ER -