  Ancel, Dobrowolski, and Grabowski (Studia Math., 1994) proved that every
countable discrete subgroup of the additive group of a normed space is free
Abelian, hence isomorphic to the direct sum of a certain number of copies of
the additive group of the integers. In the present paper, we take a
set-theoretic approach based on the theory of elementary submodels and the
Singular Compactness Theorem to remove the cardinality constraint from their
result and prove that indeed every discrete subgroup of the additive group of a
normed space is free Abelian.
