The distributivity numbers of \(\mathcal{P}(\omega)\)/fin and its square. (English) Zbl 0943.03036

Shelah, Saharon; Spinas, Otmar

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)

MSC:

03E05	Other combinatorial set theory
06E05	Structure theory of Boolean algebras

Keywords:

distributivity number; \({\mathcal P}(\omega)/\hbox{fin}\); Mathias forcing