Topological Models of Epistemic Set Theory
Epistemic theories can be used as alternative formalizations of classical mathematics in which its constructive component can be given explicit expression. By epistemic set theory we mean set theory with classical S4 as its underlying logic and with a weakened form of extensionality, so that two sets are taken to be the same iff it is necessarily the case that they have exactly the same elements. The purpose of the present paper is to show how to construct topological models for epistemic set theory very much as has become standard for intuitionistic higher-order theories