User blog comment:Edwin Shade/How do you evaluate extended Veblen notation ?/@comment-24920136-20171020210305

there is no limit to epsilons, the ordinal you refer to is the first fixed point of the function e such that e_x = x

true there exists e_{w*160} and e_e_0, but there are also ordinals like: e_{z_0+1}

Regarding your question about mutliple arguments on the veblen function, i too was stuck for months on that problem. So i PM'd an excellent googologist for help. Here is a text-only explanation she gave me.



If the number on the end is a limit ordinal:

Take the fundamental sequence of that ordinal.

If the number on the end is 0:

Take the fundamental sequence of that ordinal.

If the rightmost nonzero number is α+1: Decrement it, then nest in the space to the right of it n times.  If the number on the end is α+1: 

Decrement it, and nest the original expression (with α instead of α+1) in the value to the right of β n times (with everything right of that 0). Note that this is similar to the one above for if the number on the end is 0.

####.

The schutte klammer symbolen  is a way to extend the veblen notation beyond SVO. Its helpful to get a grasp on LVO, though its a bit hard to give you an breadthy explanation using inline text since its a matrix style  notation, so i'll keep it short. Basically one row indicates "values" and another "places" 1 at the wth place is SVO for example. sounds cheaty since there isnt an actual wth place, but it works..

If you want a more cookbook style list of formulas, check out Denis Maksudov's blogs on fundamental sequences. This list includes Veblen Function and Klammer Symbolen   and this one is  theta style ordinal collapse  iirc, they both crawl up to the same ordinal: LVO.