PARTITIONING PRODUCTS OF RHO(OMEGA) FIN

We generalize the cardinal invariant a to products of P(omega)/fin and then sharpen the well-known inequality b less than or equal to a by p roving b less than or equal to a(lambda) for every lambda less than or equal to omega. Here a(n), for n < omega, is the least size of an inf inite partition of (P(omega)/fin)(n), a(omega) is the least size of an uncountable partition of (P(omega)/fin)(omega), and b is the least si ze of an unbounded family of functions from omega to omega ordered by eventual dominance. We also prove the consistency of b < a(n) for ever y n < omega.