User blog comment:Emlightened/Little Bigeddon/@comment-29915175-20170106020741/@comment-27513631-20170106103342

Most of the definition is technical. Basically, \(T_\alpha\) is able to decide all formulas in the language \(\{\in,(T_\beta)_{\beta<\alpha)\}\), and lil'bigeddon is the largest number we can uniquely specify in \(\{\in,(T_\beta)_{\beta\in On)\}\) in so many symbols.