# Sh:1015

• Koszmider, P., & Shelah, S. (2013). Independent families in Boolean algebras with some separation properties. Algebra Universalis, 69(4), 305–312.
• Abstract:
We prove that any Boolean algebra with the subsequential completeness property contains an independent family of size continuum. This improves a result of Argyros from the 80ties which asserted the existence of an uncountable independent family. In fact we prove it for a bigger class of Boolean algebras satisfying much weaker properties. It follows that the Stone spaces K_{\mathcal A} of all such Boolean algebras \mathcal A contains a copy of the Čech-Stone compactification of the integers \beta\mathbb{N} and the Banach space C(K_{\mathcal A}) has l_\infty as a quotient. Connections with the Grothendieck property in Banach spaces are discussed.
• published version (8p)
Bib entry
@article{Sh:1015,
author = {Koszmider, Piotr and Shelah, Saharon},
title = {{Independent families in Boolean algebras with some separation properties}},
journal = {Algebra Universalis},
fjournal = {Algebra Universalis},
volume = {69},
number = {4},
year = {2013},
pages = {305--312},
issn = {0002-5240},
doi = {10.1007/s00012-013-0227-2},
mrclass = {06E05 (03E05 46B10 54D30)},
mrnumber = {3061090},
mrreviewer = {Klaas Pieter Hart},
doi = {10.1007/s00012-013-0227-2},
note = {\href{https://arxiv.org/abs/1209.0177}{arXiv: 1209.0177}},
arxiv_number = {1209.0177}
}