Abstract: | We develop the theory of Cκ, λi, a strongly normal filter over ??κ λ for Mahlo κ. We prove a minimality result, showing that any strongly normal filter containing {x ∈ ??κ λ: |x | = |x ∩ κ | and |x | is inaccessible} also contains Cκ, λi. We also show that functions can be used to obtain a basis for Cκ, λi (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |