Order-automorphisms of normal subsets of a power set (Q1091407)

Let A be a set of subsets of an infinite set X. We consider A as ordered by the settheoretical inclusion relation. A is called normal if every permutation of X induces an order-automorphism of A (which means that A is invariant under that permutation). The author describes all order- automorphisms of A which are induced by a permutation of X in the case when A is normal. Then she describes those normal A all whose order automorphisms are induced by permutations of X.