Filtration-equivalent 1-separable abelian groups of cardinality 1

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Abstract

We show that it is consistent with ordinary set theory ZFC and the generalized continuum hypothesis that there exist two 1-separable abelian groups of cardinality 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].

MSC

20K15
20K20
20K35
20K40

Keywords

1-separable groups
Whitehead groups
Filtration equivalent groups

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