10/30/2022, 07:09 PM
(10/21/2022, 07:46 PM)bo198214 Wrote:
- I think of addition has rank 1, multiplication has rank 2, exponentiation has rank 3, and I would continue in a similar fashion to higher ranks. For non-integer ranks I would assume some smoothness moving operation k into operation k+1.
[...]
- Maybe there is no obstacle it is more about how to define this smoothness I was mentioning above.
How'd you go about it? As simply as you are stating it? I.e. something like \(f(s,y):=b[s]y\) s.t. \(f\in \mathcal C^\infty (\mathbb R^2)\)? Or you mean that a more sophisticate condition involving smoothness or the parameter \(s\) should be developed?
Btw, maybe I'd better start a new thread but, extending your suggestion, maybe we could ask for local representability as a powerseries.... since I see you have a good fluency in the math of formal powerseries I'd like to ask you about formal Ackermann-functions here.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)