User blog comment:Hyp cos/Googolisms hard to extend?/@comment-35470197-20190429101435

If you allow uncomputable googology, \begin{eqnarray*} \min \{n \in \mathbb{N} \mid \forall m \in \omega, (\aleph = \aleph_m) \to (n = m)\} \end{eqnarray*} is difficult to extend in a non-trivial way. I like this number very much, because it gives a good passing point of uncomputable googology next to BusyBeaver function.