TY - JOUR
T1 - Regular subalgebras of complete Boolean algebras
AU - Błaszczyk, Aleksander
AU - Shelah, Saharon
PY - 2001/6
Y1 - 2001/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035534341&partnerID=8YFLogxK
U2 - 10.2307/2695044
DO - 10.2307/2695044
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0035534341
SN - 0022-4812
VL - 66
SP - 792
EP - 800
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 2
ER -