# 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.
• 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.
• Current version: 1997-09-30_10 (7p) 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},
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}
}