Strong subgroup chains and the Baer-Specker group

Details Strong subgroup chains and the Baer-Specker group Strong subgroup chains and the Baer-Specker group

2009-01-15

arxiv.org/abs/0901.2291v1

Models, Modules and Abelian Groups, B. Goldsmith; R. G\"obel (Ed.) (2008) 189-200

Mathematics

Logic

12 pages

Scientific paper

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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