The number of openly generated Boolean algebras
| dc.creator | Geschke, Stefan | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2007-02-21 | |
| dc.date.accessioned | 2026-07-07T07:48:01Z | |
| dc.date.available | 2026-07-07T07:48:01Z | |
| dc.description | This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly sigma-filtered Boolean algebras. We show that for every uncountable regular cardinal kappa there are 2^kappa pairwise non-isomorphic openly generated Boolean algebras of size kappa > aleph_1 provided there is an almost free non-free abelian group of size kappa. The openly generated Boolean algebras constructed here are almost free. Moreover, for every infinite regular cardinal kappa we construct 2^kappa pairwise non-isomorphic Boolean algebras of size kappa that are tightly sigma-filtered and c.c.c. These two results contrast nicely with Koppelberg's theorem hat for every uncountable regular cardinal kappa there are only 2^{< kappa} isomorphism types of projective Boolean algebras of size kappa . | |
| dc.identifier | https://arxiv.org/abs/math/0702600 | |
| dc.identifier | http://arxiv.org/abs/math/0702600 | |
| dc.identifier | J. Symbolic Logic 73 No. 1 (2008) 151--164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124357 | |
| dc.subject | Logic | |
| dc.title | The number of openly generated Boolean algebras | |
| dc.type | text |