De Jongh’s Theorem for Intuitionistic Zermelo-Fraenkel Set Theory
Robert Paßmann · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2020
We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with respect to every intermediate logic that is complete with respect to a class of finite trees. The same results follow for constructive set theory CZF.