FILTERS, COHEN SETS AND CONSISTENT EXTENSIONS OF THE ERDÖS-DUSHNIK-MILLER THEOREM

Abstract. We present two 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, ℵω1 ̸ → (ℵω1, ω + 1)2 and consistently, 2 ℵ0 ̸ → (2 ℵ0, ω + 1) 2