arXiv subjects

Takashi Yamazoe

Publications and source records attributed to Takashi Yamazoe.

8 recordsLinked to original sources

arXiv2026

Evasion numbers via zero-prediction

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.

math.LO↗

arXiv2026

Cardinal invariants of idealized Miller null sets

This paper provides an extensive study of the $\mathscr{I}$-Miller null ideals $M_\mathscr{I}$, $σ$-ideals on the Baire space parametrized by ideals $\mathscr{I}$ on countable sets. These $σ$-ideals are associated to the idealized versions of Miller forcing in the same way that the meager ideal is associated to Cohen forcing. We compute the cardinal invariants of $M_\mathscr{I}$ for typical examples of Borel ideals $\mathscr{I}$ and show that Cichoń's Maximum can be extended by adding the uniformity and covering numbers of $M_\mathscr{I}$ for different ideals $\mathscr{I}$.

math.LO↗

arXiv2025

Cichoń's maximum with cardinals of the closed null ideal

Let $\mathcal{E}$ denote the $σ$-ideal generated by closed null sets on the reals. We show that the uniformity and the covering of $\mathcal{E}$ can be added to Cichoń's maximum with distinct values. More specifically, it is consistent that $\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathrm{non}(\mathcal{E})<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathrm{cov}(\mathcal{E})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{\aleph_0}$ holds.

math.LO↗

arXiv2025

Cichoń's maximum with evasion number

We show that the evasion number $\mathfrak{e}$ can be added to Cichoń's maximum with a distinct value. More specifically, it is consistent that $\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathfrak{e}<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{\aleph_0}$ holds.

math.LO↗

arXiv2025

Notes on slalom prediction

We study a concept of evasion and prediction associated with slaloms, called slalom prediction. This article collects ZFC-provable properties on the slalom prediction.

math.LO↗

arXiv2024

Game-theoretic variants of splitting number

We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $\mathfrak{s}$ since the corresponding cardinal invariants behave in an interesting way. We introduce three kinds of games as reasonable realizations of the combination of the notions of splitting and infinite games. Then, we consider two cardinal invariants for each game, so we define six numbers. We prove that three of them are equal to the size of the continuum $\mathfrak{c}$ and one of them is equal to the $σ$-splitting number $\mathfrak{s}_σ$, which is defined as the minimum size of a $σ$-splitting family. On the other hand, we show that the remaining two numbers are consistently different from $\mathfrak{c}$, $\mathfrak{s}$ and $\mathfrak{s}_σ$. Moreover, though the two numbers share almost the same rule of the game, we prove that they can take distinct values from each other, and hence the slight difference of the rule is actually crucial in this sense.

math.LO↗

arXiv2024

Notes on the coexistence of limit notions

We summarize the current knowledge on the three limit notions: ultrafilter-limits, closed-ultrafilter-limits and FAM-limits. Also, we consider the possibility to perform an iteration which has all the three limits and clarify the problem we face.

math.LO↗

arXiv2021

Application of Reversible Data Hiding for Printing with Special Color Inks to Preserve Compatibility with Normal Printing

We propose an efficient framework with compatibility between normal printing and printing with special color inks in this paper. Special color inks can be used for printing to represent some particular colors and specific optical properties, which are difficult to express using only CMYK inks. Special color layers are required in addition to the general color layer for printing with special color inks. We introduce a reversible data hiding (RDH) method to embed the special color layers into the general color layer without visible artifacts. The proposed method can realize both normal printing and printing with special color inks by using a single layer. Our experimental results show that the quality of the marked image is virtually identical to that of the original image, i.e., the general color layer.

cs.MM↗