Abstract
Let κ be a regular uncountable cardinal. We shall give a criterion for certain reduced products ∏α<κGα/∏α<κ<Gα of torsion-free abelian groups Gα(α<κ) to be ℵ1-free. As an application we shall show that the norm of the Chase radical is ℵ1 in ZFC, a result which was previously known only under the assumption of the continuum hypothesis 2ℵ0=ℵ1.
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