English

$\aleph_k$-free cogenerators

Group Theory 2019-09-04 v1 Logic

Abstract

We prove in ZFC that an abelian group CC is cotorsion if and only if Ext(F,C)=0\operatorname{Ext}(F,C) = 0 for every k\aleph_k-free group FF, and discuss some consequences and related results. This short note includes a condensed overview of the λˉ\bar\lambda-Black Box for k\aleph_k-free constructions in ZFC.

Cite

@article{arxiv.1909.00595,
  title  = {$\aleph_k$-free cogenerators},
  author = {Manfred Dugas and Daniel Herden and Saharon Shelah},
  journal= {arXiv preprint arXiv:1909.00595},
  year   = {2019}
}
R2 v1 2026-06-23T11:02:56.140Z