  Generalizing [ShSi:494], for every n< omega we construct a ZFC-model where
the distributivity number of r.o. (P(omega)/fin)^{n+1}, h(n+1), is smaller than
the one of r.o.(P(omega)/fin)^{n}. This answers an old problem of Balcar,
Pelant and Simon. We also show that Laver and Miller forcing collapse the
continuum to h(n) for every n<omega, hence by the first result, consistently
they collapse it below h(n)
