  We look for partition theorems for large subtrees for suitable uncountable
trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded
by a well ordering of each level. Unlike earlier works, we do not ask the
embedding to preserve the height of the tree but the equality of levels is
preserved. We get consistency results without large cardinals.
  The intention is to apply it to model theoretic problems.
