User blog comment:B1mb0w/Fundamental Sequences/@comment-5529393-20160124015439/@comment-5529393-20160206080000

Unfortunately, changing the definition of already defined terms to suit your own taste is adding ambiguity, because people won't know what version is meant when the term or notation is used. So please do not change the definition of the Veblen functions.

I have no idea why you think phi(2,0)^^w = e_{phi(2,0)+1} would be ambiguous, and I'm not sure what you mean by "has no explanatory power". Yes, the equations that you give are correct. I'm not sure how you get from there to "ambiguous or has no explanatory power". What's not correct is the equation phi(2,1) = phi(2,0)^^w.

Can you explain what you mean a little further.