 A more ambitious theory is IZF (intuitionistic ZF). An interesting feature of the development of IZF is that one must be very careful in one’s choice of axioms: some formulations of the axioms of set theory have (constructively deducible) consequences which are not considered constructively valid (such as Excluded Middle), while other (classically equivalent) formulations of the axioms appear not to have such consequences: the latter forms, obviously to be preferred for a constructive development of set theory, often are not the most familiar ones in the classical context.