The Ostaszewski square and homogeneous Souslin trees

Assume GCH and let λ denote an uncountable cardinal.

For every sequence 〈A_i | i < λ〉 of unbounded subsets of λ⁺, and every limit θ < λ, there exists some α < λ⁺ such that otp(C_α)=θ and the (i + 1)_th-element of C_α is a member of A_i, for all i < θ.

As an application, we construct a homogeneous λ⁺-Souslin tree from □_λ + CH_λ, for every singular cardinal λ.

In addition, as a by-product, a theorem of Farah and Veličković, and a theorem of Abraham, Shelah and Solovay are generalized to cover the case of successors of regulars.