Church–Kleene ordinal
Encyclopedia
In mathematics, the Church–Kleene ordinal, 
, is a large countable ordinal
. It is the smallest non-recursive ordinal
. It is named after Alonzo Church
and S. C. Kleene.
, is a large countable ordinalLarge countable ordinal
In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non-circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of relevance to proof theory still have computable ordinal...
. It is the smallest non-recursive ordinal
Recursive ordinal
In mathematics, specifically set theory, an ordinal \alpha is said to be recursive if there is a recursive binary relation R that well-orders a subset of the natural numbers and the order type of that ordering is \alpha....
. It is named after Alonzo Church
Alonzo Church
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...
and S. C. Kleene.