Fallen cardinals

We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra compPμ(μ) contains a complete subalgebra which is isomorphic to the collapse algebra CompCol(ω1, μ0 ). Consequently, adding a generic filter to the quotient algebra Pμ(μ) = P(μ)/[μ] collapses μ0 to א1. Another corollary is that the Baire number of the space U(μ) of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory.