Algebraic Ordinals

Details Algebraic Ordinals Algebraic Ordinals

2009-07-05

arxiv.org/abs/0907.0877v3

Computer Science

Formal Languages and Automata Theory

30 pages

Scientific paper

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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