The blocker A∗ of an antichain A in a finite poset P is the set of
elements minimal with the property of having with each member of A a common
predecessor. The following is done:
1. The posets P for which A∗∗=A for all antichains are characterized.
2. The blocker A∗ of a symmetric antichain in the partition lattice is
characterized.
3. Connections with the question of finding minimal size blocking sets for
certain set families are discussed