The Kaplansky test problems for aleph_1-separable groups
Logic
2009-09-25 v1 Rings and Algebras
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 .
Keywords
Cite
@article{arxiv.math/9709230,
title = {The Kaplansky test problems for aleph_1-separable groups},
author = {Paul C. Eklof and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9709230},
year = {2009}
}