Abstract: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.
Keywords: prediction principles; almost free modules; dual modules
DOI: DOI 10.14712/1213-7243.2015.150
AMS Subject Classification: 13B10 13B35 13C13 13J10 13L05