Abstract

We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra contains a complete subalgebra which is isomorphic to the collapse algebra CompCol. Consequently, adding a generic filter to the quotient algebra collapses μ0 to 1. Another corollary is that the Baire number of the space U of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory