Initial Thinking
Forest (hypertree) functions could be used to count trees.
Forest numbers would be equivilant to ordinality.
Then
I found a post from @hyp_cos TREE into SVG.
I then found this gem from @hyp_cos which states:
- When we go through all the forests, we get a limit of ε0.
- Using forests and self-loops, we get ε1.
- Using forests and no-fused cycles, we get ϑ(Ωω), or SVO.
- The set of forests made from them (you can use different cycle-one-edge-fusing-trees) reaches BHO.
This seems to confirm my initial thinking regarding the correlation of tree : forest.
Currently
Working on a jungle number extension such that jungle numbers (considering a jungle to be an inaccessible hyperforest) would map to cardinality.
Also working on the correlation of rose numbers/functions.
Links
- http://googology.wikia.com/wiki/Subcubic_graph_number
- http://googology.wikia.com/wiki/User_blog:Hyp_cos/TREE_into_SCG_without_diamond_graph_minor
- http://googology.wikia.com/wiki/User_blog:Hyp_cos/SCG(n)_and_some_related
- https://en.wikipedia.org/wiki/Rose_tree">https://en.wikipedia.org/wiki/Rose_tree