# Sh:920

• Göbel, R., & Shelah, S. (2009). \aleph_n-free modules with trivial duals. Results Math., 54(1-2), 53–64.
• 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}
}