# Sh:855

• Shelah, S., & Strüngmann, L. H. (2010). Filtration-equivalent \aleph_1-separable abelian groups of cardinality \aleph_1. Ann. Pure Appl. Logic, 161(7), 935–943.
• Abstract:
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.
• published version (9p)
Bib entry
@article{Sh:855,
author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.},
title = {{Filtration-equivalent $\aleph_1$-separable abelian groups of cardinality $\aleph_1$}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {161},
number = {7},
year = {2010},
pages = {935--943},
issn = {0168-0072},
mrnumber = {2601022},
mrclass = {20K20},
doi = {10.1016/j.apal.2009.12.001},
note = {\href{https://arxiv.org/abs/math/0612241}{arXiv: math/0612241}},
arxiv_number = {math/0612241}
}