Abstract
ABSTRACT We prove that the Baer-Specker group Π = contains a pure subgroup isomorphic to the direct sum of 2 0 copies of itself. We produce 2 ℵ 0 nonisomorphic subgroups of Π, each isomorphic to its dual group. Finally, we show that the isomorphism type of a generalized product of ℤ's, the set of functions I → ℤ with support of size at most α, uniquely determines both the cardinality of I and α (as long as there are no measurable cardinals ≤α). All three of these results are obtained using set-theoretic existence theorems, namely, the existence of large independent families, large almost disjoint families, and Δ-systems.
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