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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:
03E17 Cardinal characteristics of the continuum
06E05 Structure theory of Boolean algebras
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