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

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