### 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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