A note on blockers in posets
  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. 
Anders Bj\"orner, Axel Hultman