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The distributivity numbers of finite products of P(omega) /fin

Saharon Shelah·Otmar Spinas
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Abstract

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)

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Saharon Shelah, Otmar Spinas. 1998-01-15. The distributivity numbers of finite products of P(omega) /fin. https://arxiv.org/abs/math/9801151

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