Sh:558

• Geschke, S., & Shelah, S. (2008). The number of openly generated Boolean algebras. J. Symbolic Logic, 73(1), 151–164. arXiv: math/0702600 DOI: 10.2178/jsl/1208358746 MR: 2387936
• 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.

• Version 2007-07-03_11 (12p) published version (15p)

@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}
}