Filtration equivalent aleph_1-separable abelian groups of cardinality   aleph_1
  We show that it is consistent with ordinary set theory ZFC and the generalized continuum hypothesis that there exist two separable abelian groups of cardinality aleph_1 which are filtration equivalent and one is a Whitehead group but the other is not. This solves one of the open problems of Eklof and Mekler. 
Saharon Shelah and Lutz Str\"ungmann