# Sh:558

• Geschke, S., & Shelah, S. (2008). The number of openly generated Boolean algebras. J. Symbolic Logic, 73(1), 151–164.
• Abstract:

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.

• Version 2007-07-03_11 (12p) published version (15p)
Bib entry
@article{Sh:558,
author = {Geschke, Stefan and Shelah, Saharon},
title = {{The number of openly generated Boolean algebras}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {73},
number = {1},
year = {2008},
pages = {151--164},
issn = {0022-4812},
mrnumber = {2387936},
mrclass = {06E05 (03G05)},
doi = {10.2178/jsl/1208358746},
note = {\href{https://arxiv.org/abs/math/0702600}{arXiv: math/0702600}},
arxiv_number = {math/0702600}
}