The number of openly generated Boolean algebras
Abstract
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 .
Keywords
Cite
@article{arxiv.math/0702600,
title = {The number of openly generated Boolean algebras},
author = {Stefan Geschke and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0702600},
year = {2007}
}