Regular subalgebras of complete Boolean algebras

Aleksander Błaszczyk*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)792-800
Number of pages9
JournalJournal of Symbolic Logic
Volume66
Issue number2
DOIs
StatePublished - Jun 2001

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