PCF and Abelian Groups
Abstract
We deal with some pcf investigations mostly motivated by abelian group theory problems and deal their applications to test problems (we expect reasonably wide applications). We prove almost always the existence of aleph_omegafree abelian groups with trivial dual, i.e. no nontrivial homomorphisms to the integers. This relies on investigation of pcf; more specifically, for this we prove that "almost always" there are F subseteq lambda^kappa which are quite free and has black boxes. The "almost always" means that there are strong restrictions on cardinal arithmetic if the universe fails this, the restrictions are "everywhere". Also we replace Abelian groups by Rmodules, so in some sense our advantage over earlier results becomes clearer.
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0710.0157
 Bibcode:
 2007arXiv0710.0157S
 Keywords:

 Mathematics  Logic;
 Mathematics  Group Theory;
 03E04;
 03E75