             Another version of Zorn’s Lemma can be given in terms of collections of sets. Given a collection \(\sH\) of sets, let us call a nest in \(\sH\) any subcollection \(\sN\) of \(\sH\) such that, for any pair of members of \(\sN\), one is included in the  other.[10]  Call \(\sH\) strongly inductive if the union of any nest in \(\sH\) is a member of \(\sH\).  Zorn’s Lemma may then be equivalently restated as the assertion that any nonempty strongly inductive collection \(\sH\) of sets has a maximal member, that is, a member properly included in no member of \(\sH\).  This may in turn be formulated in a dual form. Call a family of sets strongly reductive if it is closed under intersections of nests. Then any nonempty strongly reductive family of sets has a minimal element, that is, a member properly including no member of the family.