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)
Categories: math.LO