The distributivity numbers of finite products of ${\cal P}(\omega)$/fin

by Shelah and Spinas. [ShSi:531]
Fund. Math., 1998
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)/ hbox {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)


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