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Distributivity of quotients of countable products of Boolean algebras. (English) Zbl 1214.03032
Let Fin be the ideal of functions in $$^\omega\!A$$ which are 0 except at finitely many places. The author determines the distributivity number $${\mathfrak h}({}^\omega\!A/\text{Fin})$$ for several Boolean algebras $$A$$. Thus $${\mathfrak h}({}^\omega{\mathcal P}(\omega))={\mathfrak h}$$. The number $${\mathfrak h}(^\omega({\mathcal P}(\omega)/\text{Fin})/\text{Fin}$$ is consistently less than $${\mathfrak c}$$. This is the main result of the paper.

MSC:
 3e+17 Cardinal characteristics of the continuum 600000 Structure theory of Boolean algebras