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Keywords:
two cardinal splitting
two cardinal splitting
Summary:
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.
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