Abstract: We introduce and study a version of the classical splitting numbers \mathfrak{s}(\kappa) with two parameters \kappa\leq\lambda denoted by \mathfrak{s}(\kappa,\lambda) and defined as the minimal size of a family \mathcal S of subsets of \lambda such that for every subset A of \lambda of size \kappa there is an S\in\mathcal S such that |A\cap S|=|A\setminus S|=\kappa. We focus on the cases when \kappa=\mu^+ and \lambda=\mu^{++}. We give several results that only depend on cardinal arithmetic, in particular, on the value that 2^{\kappa} assumes.
Keywords: two cardinal splitting
DOI: DOI 10.14712/1213-7243.2025.015
AMS Subject Classification: 03E10 03E17 03E05