Regular subalgebras of complete Boolean algebras

by Blaszczyk and Shelah. [BzSh:640]
J Symbolic Logic, 2001
It is shown that there exists a complete, atomless, sigma-centered Boolean algebra, which does not contain any regular countable subalgebra if and only if there exist a nowhere dense ultrafilter. Therefore the existence of such algebras is undecidable in ZFC.

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