## FANDOM

10,661 Pages

An ordinal is called to be admissible if $$L_\alpha$$ is an admissible set, where $$L$$ is Gödel's constructible universe.[1] For successor ordinal $$\alpha$$, $$1+\alpha$$-th admissible ordinal is denoted by $$\omega_\alpha^\text{CK}$$. For example, $$\omega_\omega^\text{CK}$$ is not admissible but it is a limit of admissibles.

It is believed that $$f_{\omega_\alpha^\text{CK}}(n)$$ is approximated to $$\Sigma_\alpha(n)$$, the $$\alpha$$-th order busy beaver function using some unspecified system of fundamental sequences. Due to many ways of defining fundamental sequences and busy beaver functions with oracles it may be not true.

## Sources

1. Gostanian, Richard. The next admissible ordinal.