Filtration equivalent aleph_1-separable abelian groups of cardinality aleph_1
Logic
2016-08-16 v1
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 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.
Cite
@article{arxiv.math/0612241,
title = {Filtration equivalent aleph_1-separable abelian groups of cardinality aleph_1},
author = {Saharon Shelah and Lutz Strüngmann},
journal= {arXiv preprint arXiv:math/0612241},
year = {2016}
}