In classical set theory, Zorn's Lemma is equivalent to the axiom of choice and a host of other principles and theorems. But in intuitionistic set theory (IZF), in which the law of excluded middle is not assumed, the situation is quite different. (A presentation of IZF may be found in Chapter VIII of [3].) Here, Zorn's lemma turns out to be remarkably weak: not only does it fail to imply the axi...