05/26/2022, 11:33 PM
(05/26/2022, 09:04 PM)tommy1729 Wrote:
\[f(x , s-1 , f(x , s , y)) = f(x , s, f(y , s-1 , 1))\]
\[f(x , s , f(y , s-1 , z)) = f(f(x , s , y) , s-1 , f(x , s , z))\]
solved simultan.
Forgive me the off-topic in the off-topic. But I highlight how much we would profit conceptually to have an unifying framework/language to treat, express/compare all the questions of this kind.
Notice how asking that a solution to Bennett equation can be modified into something that satisfies Goodstein would need and use the same framework. Same goes for the question of how all the various hyperoperations (lower, offsets, ackermann...) do compare with each other.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)