Cardinal Invariants and Rosenthal families

Rosenthal's lemma is a classical result that concerns sequences of measures on pairwise disjoint sets and a Rosenthal family is a collection of infinite subsets of the natural numbers that can replace the collection of all infinite subsets of natural numbers in Rosenthal's lemma. In this talk we will see that all ultrafilters are Rosenthal families and that the minimal cardinality of a Rosenthal family is r, where r is the reaping number.