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.
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