10/23/2022, 09:19 PM
(10/18/2022, 05:40 AM)Shanghai46 Wrote: Also, there's no real nice property we would use to easely extend fractional iterations and ranks of hyperoperations. Like associativity or commutativity.
@Shanghai
I agree Shanghai. The absence of such a condition relating fractional ranks seems to be the biggest obstacle. I tried to begin a little exploration of the problem and its possible solutions here [2022] but I'm still far from a decent solution. Probably the real condition needed is non-algebraic but topological/differential, as bo198214 is suggesting here when he says
Quote:Maybe there is no obstacle it is more about how to define this smoothness I was mentioning above.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)