  An algebraic tree T is one determined by a finite system of fixed point
equations. The frontier \Fr(T) of an algebraic tree t is linearly ordered by
the lexicographic order \lex. When (\Fr(T),\lex) is well-ordered, its order
type is an \textbf{algebraic ordinal}. We prove that the algebraic ordinals are
exactly the ordinals less than $\omega^{\omega^\omega}$.
