 By using a Skolemization of the theory of dimension groups, we can embed "E(Ω)" functorially into a dimension vector space "F(Ω)".The vector space counterexample of the theorem above is "G=F(Ω)", for any set Ω with at least ℵ2 elements.This counterexample has been modified subsequently by Ploščica and Tůma to a direct semilattice construction.