Strong subgroup chains and the Baer-Specker group
Logic
2009-01-16 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.0901.2291,
title = {Strong subgroup chains and the Baer-Specker group},
author = {Oren Kolman},
journal= {arXiv preprint arXiv:0901.2291},
year = {2009}
}
Comments
12 pages