Isomorphism Types of Trees
Haim Gaifman, Ernst P. Specker · Birkhäuser Basel eBooks · 1990
A tree is a partially ordered system 〈A, ≦〉 such that for every x∈A the set Px = {y | yx} is well ordered by ≦. The rankp(x) of x is the order type of Px (this is an ordinal number). The rank ρ(T) of the tree is the least upper bound of ρ(x), x∈A. For every ordinal α, Rα(T), or simply, Rα, is the set of all elements of rank α.