Madore's ψ function

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Madore's \(\psi\) function is a function for expressing extremely large countable ordinals.

Defination

Madore's \(\psi\) function is defined as follows:

\(S=\{0,1,\omega,\Omega\}\) is our tool box.

\(C(0)=\)all of the things you can make from S and finite applications of \(+\times\)^ in S.

\(C(n+1)=\) all of the things you can make from \(C(n)\) and finite applications of \(+\times\)^\(\psi\) in \(C(n)\).

\(\psi(n)=\) the first countable ordinal not in \(C(n)\).


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