Stationary subsets of [ℵω]<ωn

Abstract

AbstractIn this paper, assuming large cardinals, we prove the consistency of the following:Let n ∈ ω and k1, k2 ≤ n. Let f: ω → {k1, k2} be such that for all n1 < n2 ∈ f−1{k1},n2 − n1 ≥ 4. Then the setis stationary in The above is equivalent to the statement that for any structure on on ℵω, there is ≺ A such that ∣∣ = ωn and for all m > n, cf( ∩ ωm) = ωf(m).