Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o., 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).
@article{bwmeta1.element.bwnjournal-article-fmv158i1p81bwm,
author = {Saharon Shelah and Otmar Spinas},
title = {The distributivity numbers of finite products of P($\omega$)/fin},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {81-93},
zbl = {0949.03044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv158i1p81bwm}
}
Shelah, Saharon; Spinas, Otmar. The distributivity numbers of finite products of P(ω)/fin. Fundamenta Mathematicae, Tome 158 (1998) pp. 81-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv158i1p81bwm/
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