  'Skolem arithmetic' is the complete theory $T$ of the multiplicative monoid
$(\mathbb{N},\cdot)$. We give a full characterization of the
$\varnothing$-definable stably embedded sets of $T$, showing in particular
that, up to the relation of having the same definable closure, there is only
one non-trivial one: the set of squarefree elements. We then prove that $T$ has
weak elimination of imaginaries but not elimination of finite imaginaries.
