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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