Filtration equivalent aleph1-separable abelian groups of cardinality aleph1
Saharon Shelah, Lutz Strüngmann
Abstract
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 aleph1 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.
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