### Independent families in Boolean algebras with some separation properties

by Koszmider and Shelah. [KsSh:1015]

Algebra Universalis, 2013

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_A
of all such Boolean algebras A contains a copy of the
Cech-Stone compactification of the integers
beta {N} and the Banach space C(K_A) has
l_infty as a quotient. Connections with the Grothendieck property
in Banach spaces are discussed.

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