Evasion numbers via zero-prediction

Takashi Yamazoe

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arXiv · 2605.26611

Evasion numbers via zero-prediction

Takashi Yamazoe

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Abstract

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.

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BibTeX RIS

Takashi Yamazoe. 2026-05-26. Evasion numbers via zero-prediction. https://arxiv.org/abs/2605.26611

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