A canonical partition theorem for trees

Abstract

In this paper we prove a canonical partition theorem for weakly embedded subtrees of a given regular tree. It was brought to my attention that there is a paper of Milliken "Canonical partition theorem for strongly embedded subtrees of regular trees" circulated in the 1980's. This paper is still unpublished and the results in my paper are discovered independently. Although it is possible to conclude the result about weakly embedded subtrees from Milliken's paper, we give a direct proof which works for both, weakly and strongly embedded subtrees.