Filtration-equivalent -separable abelian groups of cardinality

We show that it is consistent with ordinary set theory Z F C and the generalized continuum hypothesis that there exist two ℵ 1 -separable abelian groups of cardinality ℵ 1 which are filtration-equivalent and one is a Whitehead group but the other is not. This solves one of the open problems from Eklof and Mekler (2002) [2].