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Preprint Number 706
706. Saharon Shelah Quite free complicated abelian group, PCF and Black Boxes E-mail: 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: |

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