## FANDOM

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Using Madore's psi function, the ordinal $$\psi(\Omega_{\omega})$$ is a large countable ordinal that is the proof theoretic ordinal of $$\Pi_1^1$$-$$\text{CA}_0$$, a subsystem of second-order arithmetic.

The subcubic graphs, which are used in definition of SCG function, can be ordered so that we can make bijection between them and ordinals below $$\psi(\Omega_{\omega})$$, as well as Buchholz hydras with $$\omega$$ labels removed.[1]

It is the first ordinal $$\alpha$$ for which $$g_{\alpha}(n)$$ in the slow-growing hierarchy catches up with $$f_{\alpha}(n)$$ the fast-growing hierarchy, under the most common usage.