Algebraic Ordinals
Stephen L. Bloom, Zoltán Ésik · Fundamenta Informaticae · 2010
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 <e If (Fr(T) <e) is well-ordered, its order type is an algebraic ordinal. We prove that the algebraic ordinals are exactly the ordinals less than ω$^{ω}$$^{ω}$.