Independent families in Boolean algebras with some separation properties
Logic
2012-09-04 v1 Functional Analysis
General Topology
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 as a quotient. Connections with the Grothendieck property in Banach spaces are discussed.
Keywords
Cite
@article{arxiv.1209.0177,
title = {Independent families in Boolean algebras with some separation properties},
author = {Piotr Koszmider and Saharon Shelah},
journal= {arXiv preprint arXiv:1209.0177},
year = {2012}
}