### \$\aleph_n\$-free modules with trivial dual

by Goebel and Shelah. [GbSh:920]
Results in Math, 2009
In the first part of this paper we introduce a simplified version of a new Black Box from Shelah [Sh:883] which can be used to construct complicated aleph_n-free abelian groups for any natural number n in N . In the second part we apply this prediction principle to derive for many commutative rings R the existence of aleph_n-free R-modules M with trivial dual M^*=0, where M^*= Hom (M,R) . The minimal size of the aleph_n-free abelian groups constructed below is beth_n, and this lower bound is also necessary as can be seen immediately if we apply GCH.

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