User blog comment:B1mb0w/J Function Sandpit J 4/@comment-5529393-20151014104445/@comment-10262436-20151101100249

Hi Deeedlit11 The link to "The Ordinal Calculator" leads to a detailed paper which uses a different rules to those you listed above. Key differences being:

phi(0, b+1) [n] = phi(0,1)^(phi(0, b)) = w^^(b+1) phi(a+1, 0) [0] = 0    i.e. no change phi(a+1, 0) [n+1] = phi(a, phi(a+1, 0)[n] + 1)

Therefore phi(2,0)[1] = phi(1,1) = epsilon_1 and phi(2,0)[2] = phi(1,phi(1,1)+1)

I had thought there would be general agreement on rules of this sort. Appreciate any further comments you may have.