User blog comment:B1mb0w/FGH of Omega/@comment-27513631-20160608172607/@comment-10262436-20160613122040

Hi. Not sure why you say Veblen can be defined in 1 or 2 lines. I have not seem any definition smaller than a dozen lines or more. To make matters worse, there seems to be no universal agreement on the fundamental sequences to use for veblen and hence there are competing definitions that only complicate things further.

Even if you can define veblen in 2 lines, you still need to incorporate FGH definitions (say 3 lines) to apply veblen in a FGH function before you construct large finite numbers (using the transfinite ordinals 'scaffolding'). Therefore there is an interesting advantage that using just 3 lines of FGH applied to omega as well, will give you equivalent large numbers, with less theoretical baggage. This is not quite true if the FGH of omega notation runs out of steam at phi(w,0) which it seems it does.

BTW

I have spent a lot of time, trying to work around these hurdles, and create a function with minimal defining rules which still grows at a very fast rate:  SVO, LVO and beyond, etc. My lastest blog on the S Function (Version 2) may be close to the mark. The S function is based on the observations above, and I think I have been able to generalise the defining rules to well beyond phi(w,0), SVO and LVO. Interested in your thoughts, if you have a moment.