On the cofinalities of Boolean algebras and the ideal of null sets

by

Krzysztof Ciesielski, and J. Pawlikowski

Algebra Universalis 47(2) (2002), 139-143.

We will show that if the cofinality of the ideal of Lebesgue measure zero sets is equal to \omega_1 then there exists a Boolean algebra B of cardinality \omega_1 which is not a union of strictly increasing \omega-sequence of its subalgebras. This generalizes a result of Just and Koszmider who showed that it is consistent with ZFC+\neg CH that such an algebra exists.