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JSYML
2008

The number of openly generated Boolean algebras

13 years 11 months ago
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 .
Stefan Geschke, Saharon Shelah
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JSYML
Authors Stefan Geschke, Saharon Shelah
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