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Algebraic Ordinals
Published 5 Jul 2009 in cs.FL and cs.LO | (0907.0877v3)
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 \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 $\omega{\omega\omega}$.
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