 
Summary: Logic in topoi:
Functorial semantics for higherorder logic
Dissertation Abstract
Steven Awodey
The University of Chicago
Winter 1997
This dissertation investigates what may be termed the model theory of
higherorder logic using the methods of category theory. Of course, there
is no such field of logic as ``higherorder model theory,'' and so our first con
cern in chapter I will be to specify the basic objects under investigation, viz.
higherorder logical theories and their models. This is a fairly straightforward
generalizationin two different directionsof the familiar corresponding no
tions for firstorder logic: the notion of a logical theory is generalized from
first to higherorder logic, and the notion of a model is generalized both
from first to higherorder logic, and from the category Sets to arbitrary
topoi. 1 The remaining four chapters of the dissertation are then devoted to
what may be termed `functorial semantics for higherorder logic,' or `topos
semantics,' by which is meant the study of such higherorder logical theories
and their models by functorial methods, i.e. employing the theory of cate
gories and functors, invented by S. Eilenberg and S. Mac Lane (cf. [3]), and
