Yusuke Hayashi

collaborators

4 papers

math.LO2025

Stationary list colorings

Yusuke Hayashi

Komjath studied the list chromatic number of infinite graphs and introduced the notion of restricted list chromatic number. For a graph $X = (V_{X}, E_{X})$ and a cardinal $I^º$ , we say th…

math.LO2025

Dominating numbers at singular cardinals

Yusuke Hayashi

We study the generalized dominating number $d_{I^} ¼$ at a singular cardinal $I^¼$ of cofinality $I^º$ . We show two lower bounds: in ZFC, $\mathrm{cf}([Î¼]^Îº,\subseteq) \leq…

cs.AI2025

Universal AI maximizes Variational Empowerment

Yusuke Hayashi, Koichi Takahashi

This paper presents a theoretical framework unifying AIXI -- a model of universal AI -- with variational empowerment as an intrinsic drive for exploration. We build on the existing…

math.LO2024

Game-theoretic variants of splitting number

Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi +1

We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $s$ since the corresponding cardinal in…