Xi function

Xi function is extremelly fast growing function defined by Adam P. Goucher

Definition
Consider SKI calculus extended with oracle combinator Ω  such that tree Ω(x(yz))   β- redeces to tree y iff tree x  β- redeces to single I combinator , and  β- reduces to tree z otherwise. Then function  Ξ(n) is size of largest tree being normal form of well-founded tree of size at most n.

This function is uncomputable and extremelly fast-growing. It's corresponding ordinal is smallest ordinal such that /alpha=/omega_/alpha^{CK}. Number  Ξ(10^6) is larger than any number defined before.