Universal dendrites for some families of dendrites with a countable set of end points

We prove that for any countable ordinal α ⩾ 1 (and for any integer κ ⩾ 3 ), there exists a universal dendrite in the family of all dendrites (of orders ⩽κ) with a closed countable set of end points such that the α-derivative of the set of end points contains at most one point.