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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.26611 |
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| _version_ | 1866916047220637696 |
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| author | Yamazoe, Takashi |
| author_facet | Yamazoe, Takashi |
| contents | Cruz Chapital, Goto, Hayashi and the author showed that the game-theoretic variants $\mathfrak{s}_{\mathrm{game}^*}^\mathrm{I}$ and $\mathfrak{s}_{\mathrm{game}^{**}}^\mathrm{I}$ of the splitting number $\mathfrak{s}$ are consistently different, although the corresponding two games differ only in a minor case. This result suggests that even if two relational systems $\mathbf{R}=\langle X,Y,\sqsubset\rangle$, $\mathbf{R}^\prime=\langle X,Y,\sqsubset^\prime\rangle$ are the same modulo a countable set $C\subseteq X$, the associated cardinal invariants might be different. We study this phenomenon for the standard relational system of evasion and prediction and for a variation of it. We show that such a difference occurs for the standard one, but not for the variation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Evasion numbers via zero-prediction Yamazoe, Takashi Logic 03E17, 03E35 Cruz Chapital, Goto, Hayashi and the author showed that the game-theoretic variants $\mathfrak{s}_{\mathrm{game}^*}^\mathrm{I}$ and $\mathfrak{s}_{\mathrm{game}^{**}}^\mathrm{I}$ of the splitting number $\mathfrak{s}$ are consistently different, although the corresponding two games differ only in a minor case. This result suggests that even if two relational systems $\mathbf{R}=\langle X,Y,\sqsubset\rangle$, $\mathbf{R}^\prime=\langle X,Y,\sqsubset^\prime\rangle$ are the same modulo a countable set $C\subseteq X$, the associated cardinal invariants might be different. We study this phenomenon for the standard relational system of evasion and prediction and for a variation of it. We show that such a difference occurs for the standard one, but not for the variation. |
| title | Evasion numbers via zero-prediction |
| topic | Logic 03E17, 03E35 |
| url | https://arxiv.org/abs/2605.26611 |