## Journal of Symbolic Logic

### Regular Subalgebras of Complete Boolean Algebras

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746473

Mathematical Reviews number (MathSciNet)
MR1833478

Zentralblatt MATH identifier
0992.06013

JSTOR