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By Algebraic Ordinals, S. L. Bloom and Z. Ésik


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. When (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 ωωω.

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