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)

@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}
}