The number of openly generated Boolean algebras

This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly -filtered Boolean algebras. We show that for every uncountable regular cardinal there are 2 pairwise non-isomorphic openly generated Boolean algebras of size > 1 provided there is an almost free non-free abelian group of size . The openly generated Boolean algebras constructed here are almost free. Moreover, for every infinite regular cardinal we construct 2 pairwise non-isomorphic Boolean algebras of size that are tightly -filtered and c.c.c. These two results contrast nicely with Koppelberg's theorem in [13] that for every uncountable regular cardinal there are only 2< isomorphism types of projective Boolean algebras of size .

• Type: Journal
• Year: 2008
• Where: JSYML
• Authors: Stefan Geschke, Saharon Shelah
• Keywords: Boolean Algebras, JSYML 2008, Projective Boolean Algebras, Regular Cardinal