Geodesic
Separable $\aleph_k$-free modules with almost trivial dual
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 7-20.

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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.
DOI : 10.14712/1213-7243.2015.150
Classification : 13B10, 13B35, 13C13, 13J10, 13L05
Keywords: prediction principles; almost free modules; dual modules 
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Herden, Daniel; Pedroza, Héctor Gabriel Salazar. Separable $\aleph_k$-free modules with almost trivial dual. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 7-20. doi : 10.14712/1213-7243.2015.150. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.150/

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