User blog:C7X/Notes

Let $$\gamma^{(+^\delta)}$$ denote the + operation applied $$\delta$$ times to $$\gamma$$.

For $$\gamma\in\textrm{Ord}$$, define $$\textrm{GSU}(\gamma):=\textrm{max}(\{\delta:L_\gamma\prec_{\Sigma_1}L_\delta\}\cup\{0\})$$ (GSU stands for "greatest stable up to")

For $$\gamma\in\textrm{Ord}$$, here let $$\gamma^*:=\textrm{min}(\{\delta >\gamma:\textrm{max}(\{\xi:\exists\delta'(\textrm{GSU}(\delta)=\delta'^{(+^\xi)})\})>\textrm{max}(\{\theta:\exists\gamma'(\textrm{GSU}(\gamma)=\gamma'^{(+^\theta)})\})\})$$

$$B(X,\beta)\cap\pi\subseteq\beta$$