  Let us denote by $\mathcal{SOMP}$ the class of all set-representable
orthomodular posets and by $\mathcal{PD SOMP}$ those elements of
$\mathcal{SOMP}$ in which any pair of points in the underlying set $P$ can be
distinguished by a set (i.e., $(P, \mathcal{L}) \in \mathcal{PD SOMP}$
precisely when for any pair $x, y \in P$ there is a set $A \in \mathcal{L}$
with $x \in A$ and $y \notin A$).
  In this note we first construct, for each $(P, \mathcal{L}) \in
\mathcal{SOMP}$, a point-distinguishing orthomodular poset that is isomorphic
to $(P, \mathcal{L})$. We show that by using a generalized form of the Stone
representation technique we also obtain point-distinguishing representations of
$(P, \mathcal{L})$. We then prove that this technique gives us
point-distinguishing representations on which all two-valued states are
determined by points (all two-valued states are Dirac states).
  Since orthomodular posets may be regarded as abstract counterparts of event
structures about quantum experiments, results of this work may have some
relevance for the foundation of quantum mechanics.
