# Sh:531

- Shelah, S., & Spinas, O. (1998).
*The distributivity numbers of finite products of {\mathcal P}(\omega)/\mathrm{fin}*. Fund. Math.,**158**(1), 81–93. arXiv: math/9801151 MR: 1641157 -
Abstract:

Generalizing [ShSi:494], for every n<\omega we construct a ZFC-model where the distributivity number of r.o.({\mathcal P}(\omega)/\textrm{fin})^{n+1}, {\bf h}(n+1), is smaller than the one of r.o.({\mathcal P}(\omega)/\textrm{fin})^{n}. This answers an old problem of Balcar, Pelant and Simon. We also show that Laver and Miller forcing collapse the continuum to {\bf h}(n) for every n< \omega, hence by the first result, consistently they collapse it below {\bf h}(n) - Version 1998-01-22_10 (11p) published version (13p)

Bib entry

@article{Sh:531, author = {Shelah, Saharon and Spinas, Otmar}, title = {{The distributivity numbers of finite products of ${\mathcal P}(\omega)/\mathrm{fin}$}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {158}, number = {1}, year = {1998}, pages = {81--93}, issn = {0016-2736}, mrnumber = {1641157}, mrclass = {03E05 (03E10 03E35)}, note = {\href{https://arxiv.org/abs/math/9801151}{arXiv: math/9801151}}, arxiv_number = {math/9801151} }