User blog comment:B1mb0w/Finite: a tour of the finite numbers/@comment-11227630-20160623112907/@comment-11227630-20160624022900

Indeed, we have TREE(n) grows at least as fast as $$f_{\vartheta(\Omega^\omega\omega)}(n)$$. But we still don't know which grows faster, TREE(n) or $$f_{LVO}(n)$$.

Note that LVO is $$\vartheta(\Omega^\Omega)$$, which is larger than $$\vartheta(\Omega^\omega\omega)$$.