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Keywords:
prediction principles; almost free modules; dual modules
Summary:
An $R$-module $M$ has an almost trivial dual if there are no epimorphisms from $M$ to the free $R$-module of countable infinite rank $R^{(\omega)}$. For every natural number $k>1$, we construct arbitrarily large separable $\aleph_k$-free $R$-modules with almost trivial dual by means of Shelah's Easy Black Box, which is a combinatorial principle provable in ZFC.
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