The number of openly generated Boolean algebras

Stefan Geschke*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly σ-filtered Boolean algebras. We show that for every uncountable regular cardinal κ there are 2κ pairwise non-isomorphic openly generated Boolean algebras of size κ > N1 provided there is an almost free non-free abelian group of size κ. The openly generated Boolean algebras constructed here are almost free. Moreover, for every infinite regular cardinal κ we construct 2κ pairwise non-isomorphic Boolean algebras of size κ that are tightly σ-filtered and c.c.c. These two results contrast nicely with Koppelberg's theorem in [12] that for every uncountable regular cardinal κ there are only 2 isomorphism types of projective Boolean algebras of size κ.

Original languageEnglish
Pages (from-to)151-164
Number of pages14
JournalJournal of Symbolic Logic
Volume73
Issue number1
DOIs
StatePublished - Mar 2008

Keywords

  • Almost free
  • Openly generated
  • Projective Boolean algebra
  • Tightly σ-filtered

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