Published online by Cambridge University Press: 12 March 2014
It is proved that the following conditions are equivalent:
(a) there exists a complete, atomless, σ–centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra.
(b) there exists a nowhere dense ultrafilter on ω.
Therefore, the existence of such algebras is undecidable in ZFC. In “forcing language” condition (a) says that there exists a non–trivial σ–centered forcing not adding Cohen reals.