Algebraic Ordinals

Abstract

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 <ℓ If (Fr(T) <ℓ) is well-ordered, its order type is an algebraic ordinal. We prove that the algebraic ordinals are exactly the ordinals less than ω $^{&omega;}$ $^{&omega;}$ .