Concentrated sets and $\gamma$-sets in the Miller model

Abstract

Using combinatorial covering properties, we show that there is no concentrated set of reals of size ${\omega }_2$ in the Miller model. The main result refutes a conjecture of Bartoszyński and Halbeisen. We also prove that there are no $\gamma$-set of reals of size ${\omega }_2$ in the Miller model.

arXiv commentarXiv admin note: text overlap with arXiv:2204.08257