For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$ . Furthermore, < denotes the binary operation defined inP κ λ byx (...) + denotes the setP κ λ−I, andI * the filter dual toI.An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)shrink)