Independence of Boolean algebras and forcing Original Research Article

If κ⩾ω is a cardinal, a complete Boolean algebra B is called κ-dependent if for each sequence View the MathML source of elements of B there exists a partition of the unity, P, such that each p∈P extends bβ or bβ′, for κ-many β∈κ. The connection of this property with cardinal functions, distributivity laws, forcing and collapsing of cardinals is considered.