Valentin Haberl

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20232025

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math.GN2025

Concentrated sets and the Hurewicz property

Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy

A set of reals $X$ is $b$ -concentrated if it has cardinality at least $b$ and it contains a countable set $D \subseteq X$ such that each closed subset of $X$ d…

math.GN2023

Concentrated sets and $γ$ -sets in the Miller model

Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy

Using combinatorial covering properties, we show that there is no concentrated set of reals of size $ω_{2}$ in the Miller model. The main result refutes a conjecture of Bartoszyński…

Concentrated sets and the Hurewicz property

Concentrated sets and γ-sets in the Miller model

Concentrated sets and $γ$ -sets in the Miller model