Abstract: | We show that for every uncountable regular κ and every κ-complete Boolean algebra B of density ≤ κ there is a filter F ? B such that the number of partitions of length < modulo κF is ≤2<κ. We apply this to Boolean algebras of the form P(X)/I, where I is a κ-complete κ-dense ideal on X. Mathematics Subject Classification: 06E05, 03C20. |