Circulation and the Fast-Growing Hierarchy
#20
(07/10/2022, 03:20 AM)Catullus Wrote:
(06/07/2022, 11:53 AM)MphLee Wrote:
Quote:It might be interesting to extend the hyper-operation hierarchy to transfinite ordinal ranks.
Yea, I believe that fast growing hierarchies are a tool that can be used to achieve this. If I recall correctly, I'd better check the literature, but someone important already tried to extend the lower hyperoperations to ordinals... was it by Doner and Tarski? I'll double check if needed... i have the paper somewhere.
Is it this paper An extended arithmetic of ordinal numbers?

Yes It is! Rolleyes

Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)

\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
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RE: Circulation and the Fast-Growing Hierarchy - by MphLee - 07/13/2022, 06:47 PM

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