Independence of Boolean algebras and forcing

Abstract

If κ≥ω is a cardinal, a complete Boolean algebra B is called κ-dependent if for each sequence 〈bβ: β<κ〉 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. © 2003 Elsevier B.V. All rights reserved.