Independent families in Boolean algebras with some separation properties
Independent families in Boolean algebras with some separation properties
We prove that any Boolean algebra with the subsequential completeness property contains an independent family of size $${\mathfrak{c}}$$ , the size of the continuum. This improves a result of Argyros from the 1980s, which asserted the existence of an uncountable independent family. In fact, we prove it for a bigger …