Matthew Hendtlass: Topological models of IZF

Abstract: Topological models are a special case of Heyting-valued models—the constructive counterpart to Boolean valued models and include both Beth and Kripke models. The beauty of topological models is that logical principles can be translated into topological properties (though unfortunately these tend to be very unnatural) and the construction of interesting models of constructive set theory can be reduced to the construction of interesting topological spaces.

In this talk we discuss topological models of intuitionistic ZF set theory. In particular we look at which standard nonconstructive principles can and cannot be separated using topological models.