The weak □* is really weaker than the full □

Abstract

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