e/Kleene's O

Information
has gloss	eng: In set theory and computability theory, Kleene's \mathcalO} is a canonical subset of the natural numbers when regarded as ordinal notations. It contains ordinal notations for every recursive ordinal, that is, ordinals below Church–Kleene ordinal, \omega_1^CK}. Since \omega_1^CK} is the first ordinal not representable in a computable system of ordinal notations the elements of \mathcalO} can be regarded as the canonical ordinal notations.
lexicalization	eng: Kleene's O
instance of	(noun) the number designating place in an ordered sequence ordinal number, no., ordinal