Splitting number at uncountable cardinals

Abstract

Abstract We study a generalization of the splitting number s to uncountable cardinals. We prove that 𝔰( κ ) > κ + for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption 𝔰(ℵ ω ) > ℵ ω +1 has a considerable large cardinal strength as well.