Filters, Cohen sets and consistent extensions of the Erdos-Dushnik-Miller theorem

摘要

We present tow different types of models where, for certain singular cardinals λ of uncountable cofinality. λ → (λ, ω + 1)~2, although λ is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, N_(ω_1) → (N_(ω_1)·ω + 1)~2 and consistently, 2~(N_0) → (2~(N_0)·ω + 1)~2.