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)

@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}
}