Strong subgroup chains and the Baer-Specker group

Oren Kolman (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Cotorsion; Baer–Specker group; Kaplansky invariants; abstract elementary class; infinitary logic

Domaines: Logique [math.LO]; Théorie des groupes [math.GR]; Algèbre commutative [math.AC]

Oren Kolman. Strong subgroup chains and the Baer-Specker group. B. Goldsmith; R. Göbel. Models, Modules and Abelian Groups, W. de Gruyter, pp.189-200, 2008. ⟨hal-00353206⟩