Regular subalgebras of complete Boolean algebras

Journal of Symbolic Logic 66 (2):792-800 (2001)
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Abstract

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

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Citations of this work

Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
Free Boolean algebras and nowhere dense ultrafilters.Aleksander Błaszczyk - 2004 - Annals of Pure and Applied Logic 126 (1-3):287-292.

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References found in this work

Selective ultrafilters and homogeneity.Andreas Blass - 1988 - Annals of Pure and Applied Logic 38 (3):215-255.
More on simple forcing notions and forcings with ideals.M. Gitik & S. Shelah - 1993 - Annals of Pure and Applied Logic 59 (3):219-238.

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