A canonical partition theorem for uniform families of finite strong subtrees

Abstract

Extending a result of K. Milliken \cite{Mi2}, in this paper we prove a Ramsey classification result for equivalence relations defined on uniform families of finite strong subtrees of a finite sequence $(U_i)_{i\in d}$ of fixed trees $U_i$, $i\in d$, that have a finite uniform branching but are of infinite length.