Regular Subalgebras of Complete Boolean Algebras
Blaszczyk, Aleksander ; Shelah, Saharon
J. Symbolic Logic, Tome 66 (2001) no. 1, p. 792-800 / Harvested from Project Euclid
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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.
Publié le : 2001-06-14
Classification:  
@article{1183746473,
     author = {Blaszczyk, Aleksander and Shelah, Saharon},
     title = {Regular Subalgebras of Complete Boolean Algebras},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 792-800},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746473}
}

Blaszczyk, Aleksander; Shelah, Saharon. Regular Subalgebras of Complete Boolean Algebras. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  792-800. http://gdmltest.u-ga.fr/item/1183746473/