# Sh:920

- Göbel, R., & Shelah, S. (2009).
*\aleph_n-free modules with trivial duals*. Results Math.,**54**(1-2), 53–64. DOI: 10.1007/s00025-009-0382-0 MR: 2529626 -
Abstract:

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^*={\rm 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. - Version 2009-06-07_11 (12p) published version (12p)

Bib entry

@article{Sh:920, author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon}, title = {{$\aleph_n$-free modules with trivial duals}}, journal = {Results Math.}, fjournal = {Results in Mathematics}, volume = {54}, number = {1-2}, year = {2009}, pages = {53--64}, issn = {1422-6383}, mrnumber = {2529626}, mrclass = {03E05 (03E35 13C05 20K20 20K30)}, doi = {10.1007/s00025-009-0382-0} }