Abstract

Steven Awodey The University of Chicago Winter 1997 This dissertation investigates what may be termed the model theory of higher-order logic using the methods of category theory. Of course, there is no such field of logic as "higher-order model theory," and so our first concern in chapter I will be to specify the basic objects under investigation, viz. higher-order logical theories and their models. This is a fairly straightforward generalization---in two different directions---of the familiar corresponding notions for first-order logic: the notion of a logical theory is generalized from first- to higher-order logic, and the notion of a model is generalized both from first- to higher-order logic, and from the category Sets to arbitrary topoi.

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