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<κ isomorphism types of projective Boolean algebras of size κ.
Original language | English |
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Pages (from-to) | 151-164 |
Number of pages | 14 |
Journal | Journal of Symbolic Logic |
Volume | 73 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2008 |
Keywords
- Almost free
- Openly generated
- Projective Boolean algebra
- Tightly σ-filtered