Concentrated sets in the Miller model

A set of reals X is concentrated if it is uncountable and there is a countable subset D of X such that for each open set U containing D the set X\U is countable. Using combinatorial covering properties, we show that there is no concentrated set of reals of size omega_2 in the Miller model. This result refutes a conjecture of Bartoszyński and Halbeisen. This is a joint work with Valentin Haberl and Lyubomyr Zdomskyy Preprint: https://arxiv.org/abs/2310.03864 The research was funded by the National Science Centre, Poland and the Austrian Science Found under the Weave-UNISONO call in the Weave programme, project: Set-theoretic aspects of topological selections 2021/03/Y/ST1/00122 --------------------------------------------------------- The next seminar meeting is scheduled for Wednesday, January 24.