# 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. - published version (7p)

Bib entry

@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}, doi = {10.1090/S0002-9939-98-04749-2}, mrclass = {20K20 (03C60 03E35 20K30)}, mrnumber = {1485469}, mrreviewer = {Manfred Dugas}, doi = {10.1090/S0002-9939-98-04749-2}, note = {\href{https://arxiv.org/abs/math/9709230}{arXiv: math/9709230}}, arxiv_number = {math/9709230} }