(12/18/2022, 03:00 AM)Daniel Wrote: OMG MphLee, your list is beyond amazing! While I would be happy to have the list on my web site I feel this should probably be managed as a collective resource. Also the list is damn valuable. The best previous list I had seen was Galidakis' list which he inherited from David Renfro. Galidakis had me link to the root of his math site so that folks would be encouraged to look at his research. Having an accessible list like this can improve a site's standing in Google searches.
I need to give this topic significant thought and return to this posting. I'd love to hear other's thoughts.
I will say, of Mphlee's list--it is very foundational. And focuses I'd say 60% on the foundations of hyper-operational "structures". So it's not a list on analytic approaches. I'm not discrediting this--it's just plain to see Mphlee is focused on the categorical nature of hyper-operations.
I agree with you about Galidakis, Daniel. The math isn't all there also. I suggest looking at John Gill's work, which is rather poorly documented (he's on Research Gate, and his typesetting leaves nothing but things to be desired). But John has done much more than Galidakis, and much of Galidakis is rephrasing of Gill's work. My work was actually in response to a multitude of these sources, which, seemed so damn incomplete--that I tried to prove everything from scratch in purely rigorous terms. Especially when it comes to infinite compositions. And not to toot my own horn, I proved things both of these parties claimed because their numbers worked out. And I did so with much greater generality--again, Galidakis worked on \(f:\mathbb{D} \to \mathbb{D}\), and I can generalize that to \(f:G \to G\) for arbitrary domain \(G\)--and that's just the first step in my first paper, lol.