  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.
