Shelah, Saharon; Spinas, Otmar The distributivity numbers of \(\mathcal{P}(\omega)\)/fin and its square. (English) Zbl 0943.03036 Trans. Am. Math. Soc. 352, No. 5, 2023-2047 (2000). Authors’ summary: We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length \(\omega_{2}\), the distributivity number of \({\mathcal{P}}(\omega)\)/fin is \(\omega_{2}\), whereas the distributivity number of r.o.\(({\mathcal{P}}(\omega)\)/fin)\(^{2}\) is \(\omega_{1}\). This answers a problem of Balcar, Pelant and Simon, and others. Reviewer: James Monk (Boulder) Cited in 2 ReviewsCited in 10 Documents MSC: 03E05 Other combinatorial set theory 06E05 Structure theory of Boolean algebras Keywords:distributivity number; \({\mathcal P}(\omega)/\hbox{fin}\); Mathias forcing PDF BibTeX XML Cite \textit{S. Shelah} and \textit{O. Spinas}, Trans. Am. Math. Soc. 352, No. 5, 2023--2047 (2000; Zbl 0943.03036) Full Text: DOI arXiv OpenURL