Combinatorial principles in the core model for one Woodin cardinal

We show that relative to the consistency of a supercompact cardinal does not imply . The model-theoretic transfer property ⟨ℵ1, ℵ0⟩ → ⟨ℵ ω + 1, ℵ ω ⟩ does not imply , and it is consistent to have an ultrafilter on ℵ ω + 1 which is λ-indecomposible for all ω < λ < ℵ ω .