User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-11227630-20160606064202

To make this notation computable, we may need an algorithm to determine whether $$\alpha$$ is a regular cardinal and whether $$M(\alpha)$$ is stationary in $$\beta$$, for all terms expressed by addition, $$\varphi,\ \Omega_\cdot,\ \Xi(\cdot,\cdot)$$ and $$\Psi_\cdot(\cdot,\cdot)$$ from 0 and K.

BTW, I think, without $$\varphi$$ and even $$\Omega_\cdot$$, we can still have the same strength.