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arXiv · 2310.03864

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

Valentin Haberl·Piotr Szewczak·Lyubomyr Zdomskyy
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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 Bartoszy\'{n}ski and Halbeisen. We also prove that there are no $\gamma$-set of reals of size $\omega_2$ in the Miller model.

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Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy. 2023-10-05. Concentrated sets and $\gamma$-sets in the Miller model. https://arxiv.org/abs/2310.03864

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