There are a few variants of this ordinal: * If an infinite number of pieces are allowed, the supremum is called \(\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}\). * With 3D chess, the supremum is called \(\omega_1^{\mathfrak{Ch}_3}\). * With 3D chess with an infinite number of pieces, the supremum is called \(\omega_1^_3}\). This ordinal has been proven to equal the first uncountable ordinal.