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)

@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}
}