Inaccessible cardinal

A inaccessible cardinal, is a small uncountable ordinal.

The inaccessible cardinal is following:


 * \(I_1\) is a ordinal that is equal to first omega fixed point.
 * \(I_{n+1}\) is a ordinal that is equal to next omega fixed point and the ordinal is greater than \(I_n\).
 * \(I_\alpha[n]\) = \(I_{\alpha[n]}\), if \(\alpha\) is a limit ordinal.