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arXiv:0901.2291 [math.LO]AbstractReferencesReviewsResources

Strong subgroup chains and the Baer-Specker group

Oren Kolman

Published 2009-01-15Version 1

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.

Comments: 12 pages
Journal: Models, Modules and Abelian Groups, B. Goldsmith; R. G\"obel (Ed.) (2008) 189-200
Categories: math.LO, math.GR
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