Adding the constant evasion and constant prediction numbers to Cichoń's maximum
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912333438124032 |
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| author | Cardona, Miguel A. Repický, Miroslav Shelah, Saharon |
| author_facet | Cardona, Miguel A. Repický, Miroslav Shelah, Saharon |
| contents | Let $\mathfrak{e}^\mathsf{const}_2$ be the constant evasion number, that is, the size of the least family $F\subseteq{}^ω2$ of reals such that for each predictor $π\colon {}^{<ω}2\to 2$ there is $x\in F$ which is not constantly predicted by $π$; and let $\mathfrak{v}_2^\mathsf{const}$ be the constant prediction number, that is, the size of the least family $Π_2$ of functions $π\colon {}^{<ω}2\to 2$ such that for each $x\in{}^ω2$ there is $π\inΠ_2$ that predicts constantly $x$. In this work, we show that the constant evasion number $\mathfrak{e}_2^{\mathrm{cons}}$ and the constant prediction number $\mathfrak{v}_2^\mathsf{const}$ can be added to Cichoń's maximum with distinct values. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_24185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adding the constant evasion and constant prediction numbers to Cichoń's maximum Cardona, Miguel A. Repický, Miroslav Shelah, Saharon Logic 03E05, 03E15, 03E17, 03E35, 03E40 Let $\mathfrak{e}^\mathsf{const}_2$ be the constant evasion number, that is, the size of the least family $F\subseteq{}^ω2$ of reals such that for each predictor $π\colon {}^{<ω}2\to 2$ there is $x\in F$ which is not constantly predicted by $π$; and let $\mathfrak{v}_2^\mathsf{const}$ be the constant prediction number, that is, the size of the least family $Π_2$ of functions $π\colon {}^{<ω}2\to 2$ such that for each $x\in{}^ω2$ there is $π\inΠ_2$ that predicts constantly $x$. In this work, we show that the constant evasion number $\mathfrak{e}_2^{\mathrm{cons}}$ and the constant prediction number $\mathfrak{v}_2^\mathsf{const}$ can be added to Cichoń's maximum with distinct values. |
| title | Adding the constant evasion and constant prediction numbers to Cichoń's maximum |
| topic | Logic 03E05, 03E15, 03E17, 03E35, 03E40 |
| url | https://arxiv.org/abs/2503.24185 |