  We present a strengthening of the countable Menger theorem (edge version) of
R. Aharoni. Let $ D=(V,A) $ be a countable digraph with $ s\neq t\in V $ and
let $\mathcal{M}=\bigoplus_{v\in V}\mathcal{M}_v $ be a matroid on $ A $ where
$ \mathcal{M}_v $ is a finitary matroid on the ingoing edges of $ v $. We show
that there is a system of edge-disjoint $ s \rightarrow t $ paths $ \mathcal{P}
$ such that the united edge set of the paths is $ \mathcal{M} $-independent,
and there is a $ C \subseteq A $ consists of one edge from each element of $
\mathcal{P} $ for which $ \mathsf{span}_{\mathcal{M}}(C) $ covers all the $
s\rightarrow t $ paths in $ D $.

Combinatorics