This is an announcement for the paper "Independent families in Boolean algebras with some separation" by Piotr Koszmider and Saharon Shelah.

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 of all such Boolean algebras contains a copy of the Cech-Stone compactification of the integers and the Banach space of contnuous functions on them has $l_\infty$ as a quotient. Connections with the Grothendieck property in Banach spaces are discussed.

Archive classification: math.LO math.FA math.GN

Submitted from: piotr.math@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1209.0177

or

http://arXiv.org/abs/1209.0177