PARTITION FORCING AND INDEPENDENT FAMILIES

Abstract

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of cof(N) = a = u = i < a(T) = omega(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 = omega(1) < u = a(T) = omega(2).