 
Summary: Categorical Models of Intuitionistic Theories of Sets
and Classes
H. Forssell
Carnegie Mellon University
Pittsburgh, PA
November 1, 2004
Abstract
The thesis consists of three sections, developing models of intuition
istic set theory in suitable categories. First, the categorical framework
in which models are constructed is reviewed, and the theory of all such
models, called Basic Intuitionistic Set Theory (BIST), is stated; sec
ond, we give a notion of an ideal over a category, with which one can
build a model of BIST in which a given topos occurs as the sets; and
third, a sheaf model is given of a Basic Intuitionistic Class Theory
conservatively extending BIST.
ii
Contents
1 Categories of Classes 3
1.1 Class Category . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Class Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
