Regular subalgebras of complete Boolean algebras.

Authors
Blaszczyk, A Shelah, S
Citation
A. Blaszczyk et S. Shelah, Regular subalgebras of complete Boolean algebras., J SYMB LOG, 66(2), 2001, pp. 792-800
Citations number
7
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF SYMBOLIC LOGIC
ISSN journal
00224812 → ACNP
Volume
66
Issue
2
Year of publication
2001
Pages
792 - 800
Database
ISI
SICI code
0022-4812(200106)66:2<792:RSOCBA>2.0.ZU;2-V
Abstract
It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, sigma -centered Boolean algebra, whi ch does not contain any regular. atomless, countable-subalgebra. (b) there exists a nowhere dense ultrafilter on m. 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 C ohen reals.