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Absolutely rigid systems and absolutely indecomposable groups

Paul C. Eklof·Saharon Shelah
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Abstract

We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposable in any generic extension. However, any absolutely rigid family of groups has cardinality less than the partition cardinal kappa(omega).

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Paul C. Eklof, Saharon Shelah. 2000-10-27. Absolutely rigid systems and absolutely indecomposable groups. https://arxiv.org/abs/math/0010264

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