User blog comment:MachineGunSuper/The Infinity Generator/@comment-32876686-20180114144124/@comment-32876686-20180114150340

Perhaps not in exactly this form, but your infinity 'ALEPHEN' is known in mathematics as the omega fixed point, which even has it's own article on this wiki. In addition, you wouldn't need a stronger function to surpass ALEPHEN, (and hence a different symbol), if you defined your $$Ԓ(\alpha_0,\alpha_1,\alpha_2,...)$$ function like the Veblen hierarchy.