  Let $\Gamma$ be a totally ordered group. We use Hahn's embedding theorem to
construct a totally ordered set $\Gamma\subset \Gamma_{\operatorname{sme}}$
which classifies small extensions of $\Gamma$. This small-extensions closure
$\Gamma_{\operatorname{sme}}$ is complete and plays a crucial role in the
description of equivalence classes of valuations on the polynomial ring $K[x]$
over a field $K$.
