• On modules which are self-slender

      Gobel, Rüdiger; Goldsmith, Brendan; Kolman, Oren; Universitat Duisberg Essen; Dublin Institute of Technology; Universite de Caen (University of Houston, 2009)
      This paper is an examination of the dual of the fundamental isomorphism relating homomorphism groups involving direct sums and direct products over arbitrary index sets. We prove that for every cardinal μ, with μ ℵ0 = μ, there exists a non-slender self-slender self-small group of cardinality μ+.
    • Strong subgroup chains and the Baer–Specker group

      Kolman, Oren (Walter de Gruyter, 2008)
      Examples are given of non-elementary properties that are preserved under Cfiltrations for various classes C of abelian groups. The Baer-Specker group ℤw is never the union of a chain áAa : a < dñ of proper subgroups such that ℤw/Aa is cotorsionfree. Cotorsionfree groups form an abstract elementary class (AEC). The Kaplansky invariants of ℤw/ℤ(w) are used to determine the AECs (ℤw/ℤ(w)) and (B/A), where B/A is 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.