On the kernel of intersecting families (Q1106213)

Let \({\mathcal F}\) be a t-wise s-intersecting family, i.e., \(| F_ 1\cap...\cap F_ t| \geq s\) holds for every t members of \({\mathcal F}\). Then there exists a set Y such that \(| F_ 1\cap...\cap F_ t\cap Y| \geq s\) still holds for every \(F_ 1,...,F_ t\in {\mathcal F}\). Here exponential lower and upper bounds are proven for the possible sizes of Y.