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arXiv · 0901.2291

Strong subgroup chains and the Baer-Specker group

Oren Kolman
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Abstract

Examples are given of non-elementary properties that are preserved under C-filtrations for various classes C of Abelian groups. The Baer-Specker group is never the union of a chain of proper subgroups with cotorsionfree quotients. Cotorsion-free groups form an abstract elementary class (AEC). The Kaplansky invariants of the Baer-Specker group are used to determine the AECs defined by the perps of the Baer-Specker quotient groups that are obtained by factoring the Baer-Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.

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Oren Kolman. 2009-01-15. Strong subgroup chains and the Baer-Specker group. https://arxiv.org/abs/0901.2291

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