Infinite combinatorial principles and compact cardinals

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We proved several facts in the combinatorial set theory on Pκλ={x⊂λ:|x|<κ}, the set of all subsets of λ with cardinality less than κ. For instance :(1) If the cofinality ofλis smaller thanκ, then there exists a stationary subset S of Pκλsuch that every stationary subset of S can be splitted intoλ^+many disjoint stationary sets.(2) If the cofinality ofλis not smaller thanκand there is a weakly normal ideal onPκλ, then the cardinality of PκλisMax(2^<κ,λ).(3) Suppose that the cofinality ofλis not smaller thanκand X is a subset ofPκλ. Then, X is ineffable if and only if it has the partition property.