The Kaplansky test problems for aleph1-separable groups
Paul C. Eklof, Saharon Shelah
Abstract
We answer a long-standing open question by proving in ordinary set theory, ZFC, that the Kaplansky test problems have negative answers for aleph1-separable abelian groups of cardinality aleph1. In fact, there is an aleph1-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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