User blog comment:B1mb0w/J Function Sandpit J 4/@comment-1605058-20151014132917/@comment-1605058-20151017065201

There is no "standard" definition for up-arrow notation for ordinals. There are at least two interpretations of $$\omega\uparrow\uparrow\uparrow\omega$$, one giving $$\zeta_0$$, one giving $$\Gamma_0$$, but there is no single definition of up-arrows which would be agreed upon.

As for "Does this mean f_w^^^2(2) = f_zeta-zero(2) ?", the answer is "it depends on the choice of fundamental sequences and on what w^^^2 means".

Also, what page do you mean with "my page on epsilon_0"?