User blog comment:P進大好きbot/Elementary Large Number beyond PTO(Π11-CA0)/@comment-34422464-20190603175104/@comment-35470197-20190603231310

I see. Since my best large numbers are not easy to understand for others (the computable one non-naively goes beyond transcendental integers, and the uncomputable one non-naively goes beyond Rayo's number), I sometimes try to create large numbers under such restrictions. Such attempts are also interesting for me, because I like any (well-defined) numbers.

For example, I have created the following:
 * a computable large number precisely the same as \(f_{\omega}(10 \uparrow^{10} 10)\) defined only using an inlined single formula.
 * a uncomputable large number under \(\textrm{ZFC}\) set theory