User blog comment:Emlightened/New(ish) Concept: Googological Systems/@comment-27513631-20170804212523

Heh, okay, this is actually harder than I expected.

I mean, it was never going to be easy. But apparently, the issues don't magically stop when you're part way through formalising it and get to the point where you want to make examples. Who knew?

Basically, I've had to re-rework how lexicographic orders interplay with embedding-based orders (first time had infinite descending sequences, second had almost vacuous equivalence, third seems to work for now) and am having trouble with case distinction formalisation at a type level. I'm either going to switch from the \(\lambda\) calculus to the \(\rho\) (rewriting) calculus or replace decreasing functions with monotonic functions such that case distinction is done on fixed points.

And this doesn't really make any sense to anybody else reading, does it? Oh well, if you want to know, ask. This comment is basically my version of a sigh.