Algebraic Models of Intuitionistic Theories of Sets and Classes

Steven Awodey, Henrik Forssell
This paper constructs models of intuitionistic set theory in suitable categories. First, a Basic Intuitionistic Set Theory (BIST) is stated, and the categorical semantics are given. Second, we give a notion of an ideal over a category, using 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. The paper extends the results in [2] by introducing a new and perhaps more
more » ... ew and perhaps more natural notion of ideal, and in the class theory of part three.
doi:10.1184/r1/6490847 fatcat:izdccrgqwffibo5knadieqwrg4