User blog comment:Edwin Shade/Can Chess Ordinals Produce Functions With Uncountable Growth Rates ?/@comment-1605058-20171222153040/@comment-32876686-20171222215604

\(\omega_1^{{\mathfrak{Ch}_{\!\!\!\!\sim}}_3}\) is by definition the supremum of all game values from which white can force a win in three-dimensional chess, such that there are an infinite number of pieces, or \(\omega\) pieces. Therefore, it stands to reason that \(\omega_1^{{\mathfrak{Ch}_{\!\!\!\!\sim}}_3}\) has a fundamental sequence of ordinals, which successively describe the supremum of game values in three-dimensional chess with n-pieces.