Filtration-equivalent $aleph_1$ separable abelian groups of cardinality $\aleph_1$

by Shelah and Struengmann. [ShSm:855]
Annals Pure and Applied Logic, 2010
We show that it is consistent with ordinary set theory ZFC and the generalized continuum hypothesis that there exist two aleph_1 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.


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