Cardinal coefficients associated to certain orders on ideals

We study cardinal invariants connected to certain classical orderings on the family of ideals on omega. We give topological and analytic characterizations of these invariants using the idealized version of Frechet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint families related to certain ordering on ideals.