The Kaplansky test problems for aleph_1-separable groups

Details The Kaplansky test problems for aleph_1-separable groups The Kaplansky test problems for aleph_1-separable groups

1997-09-15

arxiv.org/abs/math/9709230v1

Mathematics

Logic

Scientific paper

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 .

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