Church–Kleene ordinal

In mathematics, the Church-Kleene ordinal ω₁^CK is a large countable ordinal. It is the smallest non-recursive ordinal. It is named after Alonzo Church and S. C. Kleene.

[edit] References

Church (1938), “The constructive second number class”, Bull. Amer. Math. Soc. 44: 224-232, <http://www.ams.org/bull/1938-44-04/S0002-9904-1938-06720-1/>
Kleene, S. C. (1938), “On Notation for Ordinal Numbers”, The Journal of Symbolic Logic 3 (4): 150-155, <http://links.jstor.org/sici?sici=0022-4812%28193812%293%3A4%3C150%3AONFON%3E2.0.CO%3B2-%23>
Rogers, Hartley (1987), The Theory of Recursive Functions and Effective Computability, First MIT press paperback edition, ISBN 978-0-262-68052-3

v • d • e countable ordinals

ω · ε₀ · Feferman–Schütte ordinal Γ₀ · Ackermann ordinal · small Veblen ordinal · large Veblen ordinal · Bachmann–Howard ordinal · Church–Kleene ordinal ω₁^CK