### Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets

Let := {A1,..., Aα} be a nonempty family of nonempty and pairwise distinct subsets of a finite ground set $V\left(A\right):={\cup}_{i-1}^{a}{A}_{i}.$ . The family is called a Sperner family (or a clutter) if

for all i, j ∈ [a], i ≠ j.

A blocking set of the family is defined to be a subset B ⊆ S of a set S ⊇ V() such that

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