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Werner's set-theoretical model is one of the simplest models of CIC. Itcombines a functional view of predicative universes with a collapsed view ofthe impredicative sort Prop. However this model of Prop is so coarse that theprinciple of excluded middle holds. Following our previous work, we interpretProp into a topological space (a special case of Heyting algebra) to make themodel more intuitionistic without sacrificing simplicity. We improve on thatwork by providing a full interpretation of dependent product types, usingAlexandroff spaces. We also extend our approach to inductive types by addingsupport for lists.

An Intuitionistic Set-theoretical Model of Fully Dependent CC{\omega}