In mathematics, specifically computability and set theory, an ordinal
is said to be computable or recursive if there is a computable well-ordering of a computable subset of the natural numbers having the order type
The successor of a computable ordinal is computable, and the set of all computable ordinals is closed downwards.
An ordinal is computable if and only if it is smaller than
Since there are only countably many computable relations, there are also only countably many computable ordinals.
This set theory-related article is a stub.