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This ordinal is sometimes said to be the first impredicative ordinal,<ref>Kurt Schütte, ''Proof theory'', Grundlehren der Mathematischen Wissenschaften, Band 225, Springer-Verlag, Berlin, Heidelberg, New York, 1977, xii + 302 pp.</ref><ref>Solomon Feferman, "[https://math.stanford.edu/~feferman/papers/predicativity.pdf Predicativity]" (2002)</ref> though this is controversial, partly because there is no generally accepted precise definition of "[[predicativity|predicative]]". Sometimes an ordinal is said to be predicative if it is less than Γ<sub>0</sub>.
Any recursive path ordering whose function symbols are well-founded with order type less than that of <math>\Gamma_0</math> itself has order type <math><\Gamma_0</math>.
==References==
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