Pardon my ignorance, but isn't TREE(3) a finite number? -Dylan Thurston
It is my understanding as well that TREE(3) is finite (Proof that TREE(n) where n >= 3 is finite?).
However, I have seen statements such as:
TREE(3) is known to exceed the $\Gamma_0$-level, which is much higher than the $\epsilon_0$-level. -Source
It is also my understanding that $\omega < \epsilon_0 < \Gamma_0$ (where $\omega$, $\epsilon_0$ & $\Gamma_0$ are transfinite).
If $\Gamma_0<TREE(3)$, wouldn't that imply TREE(3) is transfinite?