User blog comment:Hyp cos/Attempt of OCF up to Stability/@comment-35470197-20181026043805/@comment-11227630-20181026050427

In the transfinite inductive definition, we first define \(C(0,\beta)\), then \(\psi_\pi(\mathbb X,0)\) where all inductive varibles of \(\mathbb X\) are 0; then define \(C(1,\beta)\), then \(\psi_\pi(\mathbb X,\alpha)\) where \(\alpha\) and all inductive varibles of \(\mathbb X\) are \(\le1\); then define \(C(2,\beta)\), then \(\psi_\pi(\mathbb X,\alpha)\) where \(\alpha\) and all inductive varibles of \(\mathbb X\) are \(\le2\); etc.

In every inductive level, \(\psi_\pi(\mathbb X,\alpha)\) are defined for many reflection instances.