Concentrated sets and $γ$-sets in the Miller model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911928153014272 |
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| author | Haberl, Valentin Szewczak, Piotr Zdomskyy, Lyubomyr |
| author_facet | Haberl, Valentin Szewczak, Piotr Zdomskyy, Lyubomyr |
| contents | 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 and Halbeisen. We also prove that there are no $γ$-set of reals of size $ω_2$ in the Miller model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03864 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Concentrated sets and $γ$-sets in the Miller model Haberl, Valentin Szewczak, Piotr Zdomskyy, Lyubomyr General Topology 03E35, 54D20, 03E75 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 and Halbeisen. We also prove that there are no $γ$-set of reals of size $ω_2$ in the Miller model. |
| title | Concentrated sets and $γ$-sets in the Miller model |
| topic | General Topology 03E35, 54D20, 03E75 |
| url | https://arxiv.org/abs/2310.03864 |