Sh:625

• Eklof, P. C., & Shelah, S. (1998). The Kaplansky test problems for \aleph_1-separable groups. Proc. Amer. Math. Soc., 126(7), 1901–1907. arXiv: math/9709230 DOI: 10.1090/S0002-9939-98-04749-2 MR: 1485469
• Abstract:
  We answer a long-standing open question by proving in ordinary set theory, ZFC, that the Kaplansky test problems have negative answers for \aleph_1-separable abelian groups of cardinality \aleph_1. In fact, there is an \aleph_1-separable abelian group M such that M is isomorphic to M\oplus M\oplus M but not to M\oplus M.
• Version 1997-09-30_11 (7p) published version (7p)

@article{Sh:625,
 author = {Eklof, Paul C. and Shelah, Saharon},
 title = {{The Kaplansky test problems for $\aleph_1$-separable groups}},
 journal = {Proc. Amer. Math. Soc.},
 fjournal = {Proceedings of the American Mathematical Society},
 volume = {126},
 number = {7},
 year = {1998},
 pages = {1901--1907},
 issn = {0002-9939},
 mrnumber = {1485469},
 mrclass = {20K20 (03C60 03E35 20K30)},
 doi = {10.1090/S0002-9939-98-04749-2},
 note = {\href{https://arxiv.org/abs/math/9709230}{arXiv: math/9709230}},
 arxiv_number = {math/9709230}
}