The distributivity numbers of finite products of $\mathcal P(ω)/{\rm fin}$
Volume 158 / 1998
Fundamenta Mathematicae 158 (1998), 81-93
DOI: 10.4064/fm-158-1-81-93
Abstract
Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o.$(P(ω)/fin)^n$, is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).
