Journal of Symbolic Logic

Regular Subalgebras of Complete Boolean Algebras

Aleksander Blaszczyk and Saharon Shelah

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It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, $\sigma$-centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on $\omega$. Therefore, the existence of such algebras is undecidable in ZFC. In "forcing language" condition (a) says that there exists a non-trivial $\sigma$-centered forcing not adding Cohen reals.

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J. Symbolic Logic, Volume 66, Issue 2 (2001), 792-800.

First available in Project Euclid: 6 July 2007

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Blaszczyk, Aleksander; Shelah, Saharon. Regular Subalgebras of Complete Boolean Algebras. J. Symbolic Logic 66 (2001), no. 2, 792--800.

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