# 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. arXiv: math/0612241 DOI: 10.1016/j.apal.2009.12.001 MR: 2601022 -
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. - Version 2009-11-18_11 (18p) 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} }