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
generalization---in two different directions---of 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

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

Collections: Mathematics