User blog comment:Wythagoras/FGH with transfinite ordinals/@comment-24509095-20140310142212/@comment-5150073-20140311154220

No, $$\phi(1,0,1) = \Gamma_1$$, the next fixed point of $$\alpha \mapsto \phi(\alpha)$$. So, it is equal to the limit:

$$\phi(1,0,0)+1$$

$$\phi(\phi(1,0,0)+1,0)$$

$$\phi(\phi(\phi(1,0,0)+1,0),0)$$