$\mathcal{U}$-compact group topologies without convergent sequences on countably cofinal torsion-free Abelian groups

Abstract

We obtain a forcing construction that shows that it is consistent that the torsion-free Abelian group $\mathbb{Q}^{(\lambda)}$ admits a Hausdorff group topology which is also $\mathcal{U}$-compact and contains no non-trivial convergent sequences, where $\lambda$ is a cardinal whose cofinality is $\omega$ and $\mathcal{U}$ is a selective ultrafilter. This answers a question posed in arXiv:1904.05928.