User blog comment:Emlightened/New(ish) Concept: Googological Systems/@comment-5529393-20170730195718

Hmm, very intriguing post. The third to last paragraph seems to cut off prematurely.

I think everyone would be interested in "formal systems geared specifically towards allowing googological notations to be encoded into the system, and then proven to be total", the issue is that we don't really know what formal systems would be useful in such an endeavor. So it would be great if you would lead the way by showing us some examples of how one would go about creating Googological Systems.

Concerning a recursive tree structure that goes up to the SVO, I suppose one could take the Extended Veblen Notation and encode it into trees, by having branches alternate between phi(a1,a2,...,an) and a1+a2+...+an. Would it be the case in this encoding that if tree A reduces to tree B, then B cannot be homeomorphically embeddable into tree A? I haven't checked. In any case, this seems somewhat clunky; maybe there is a more elegant tree recursion up to the SVO.

I'm interested in what you are thinking regarding making notations using Bar Reduction; could you go into more detail?