arXiv math/97092301997-09-15math.LOmath.RA

The Kaplansky test problems for aleph_1-separable groups

Paul C. Eklof, Saharon Shelah

发表信息：: Proc. Amer. Math. Soc. 126 No. 7 (1998) 1901--1907

英文摘要：

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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