# Sh:898

• Shelah, S. (2013). Pcf and abelian groups. Forum Math., 25(5), 967–1038.
• 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_\omega-free abelian groups with trivial dual, i.e. no non-trivial homomorphisms to the integers. This relies on investigation of pcf; more specifically, for this we prove that “almost always” there are {\mathcal F} \subseteq {}^\kappa \lambda 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, this restriction are “everywhere”. Those are irrating results; we replace Abelian groups by R-modules, so in some sense our advantage over earlier results becomes clearer.
• Version 2013-12-01_12 (60p) published version (72p)
Bib entry
@article{Sh:898,
author = {Shelah, Saharon},
title = {{Pcf and abelian groups}},
journal = {Forum Math.},
fjournal = {Forum Mathematicum},
volume = {25},
number = {5},
year = {2013},
pages = {967--1038},
issn = {0933-7741},
mrnumber = {3100959},
mrclass = {03E04 (03E75 20K20 20K30)},
doi = {10.1515/forum-2013-0119},
note = {\href{https://arxiv.org/abs/0710.0157}{arXiv: 0710.0157}},
arxiv_number = {0710.0157}
}