  Let $s_1,s_2,\ldots s_n$ be states of a general probability theory, and
$\mathcal A$ be the set of all subsets of indices $H \subset
[n]\equiv\{1,2,\ldots n\}$ such that the states $(s_j)_{j\in H}$ are jointly
perfectly distinguishable. All subsets with a single element are of course in
$\mathcal A$, and since smaller collections are easier to distinguish, if $H\in
\mathcal A$ and $L \subset H$ then $L\in \mathcal A$; in other words, $\mathcal
A$ is a so-called $\textit{independence system}$ on the set of indices $[n]$.
In this paper it is shown that every independence system on $[n]$ can be
realized in the above manner.
