Type: Article

Partition forcing and independent families

Cruz-Chapital, Jorge A.; Fischer, Vera; Guzmán, Osvaldo; Šupina, Jaroslav;

Abstract:

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of cof(N)=a=u=i<aT=?2 . In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of cof(N)=a=i=?1<u=aT=?2 .