# Sh:1015

- Koszmider, P., & Shelah, S. (2013).
*Independent families in Boolean algebras with some separation properties*. Algebra Universalis,**69**(4), 305–312. arXiv: 1209.0177 DOI: 10.1007/s00012-013-0227-2 MR: 3061090 -
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} }