Intersection numbers of families of ideals

Abstract

We study the intersection number of families of tall ideals. We show that the intersection number of the class of analytic P-ideals is equal to the bounding number \({\mathfrak{b}}\), the intersection number of the class of all meager ideals is equal to \({\mathfrak{h}}\) and the intersection number of the class of all Fσ ideals is between \({\mathfrak{h}}\) and \({\mathfrak{b}}\), consistently different from both.