Abstract.
We will show that if the cofinality of the ideal of Lebesgue measure zero sets is equal to \( \scr{w}_1 \) then there exists a Boolean algebra B of cardinality \( \scr{w}_1 \) which is not a union of strictly increasing \( \scr w \)-sequence of its subalgebras. This generalizes a result of Just and Koszmider who showed that it is consistent with \( \textrm{ZFC}+ \neg \textrm{CH} \) that such an algebra exists.
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Received November 21; accepted in final form April 12, 2001.
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Ciesielski, K., Pawlikowski, J. On the cofinalities of Boolean algebras and the ideal of null sets. Algebra univers. 47, 139–143 (2002). https://doi.org/10.1007/s00012-002-8179-y
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DOI: https://doi.org/10.1007/s00012-002-8179-y