Submission date: 10 April 2014.

Abstract:

We like to build Abelian groups (or R-modules) which on the one hand are quite free, say \aleph_{\omega + 1}-free, and on the other hand, are complicated in suitable sense. We choose as our test problem having no non-trivial homomorphism to Z (known classically for \aleph_1-free, recently for \aleph_n-free). We succeed to prove the existence of even \aleph_{\omega_1 \cdot n}-free ones. We also know other constructions of complicated Abelian groups and modules which are quite free but this is delayed. This requires building n-dimensional black goxes, which are quite free. Thus combinatorics is of self interest and we believe will be useful also for other purposes

Mathematics Subject Classification: 03E04, 03E75, 20K20, 20K30

Keywords and phrases:

Full text arXiv 1404.2775: pdf, ps).