Menger and consonant sets in the Sacks model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911232239337472 |
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| author | Haberl, Valentin Szewczak, Piotr Zdomskyy, Lyubomyr |
| author_facet | Haberl, Valentin Szewczak, Piotr Zdomskyy, Lyubomyr |
| contents | Using iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum is independent from ZFC. We also analyze the structure of Hurewicz and consonant subsets of the Cantor cube in the Sacks model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Menger and consonant sets in the Sacks model Haberl, Valentin Szewczak, Piotr Zdomskyy, Lyubomyr Logic General Topology 54A35, 03E35 Using iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum is independent from ZFC. We also analyze the structure of Hurewicz and consonant subsets of the Cantor cube in the Sacks model. |
| title | Menger and consonant sets in the Sacks model |
| topic | Logic General Topology 54A35, 03E35 |
| url | https://arxiv.org/abs/2406.05457 |