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This category contains computable numbers that cannot be estimated using fast-growing hierarchy in the form fα(n) with α made from Bachmann's ordinal collapsing function and reasonably small values of n, because they go beyond fast-growing hierarchy with Bachmann's ordinal collapsing function.

The lower bound of this category is $$f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\psi_2(0))}^2(10)$$ with respect to Buchholz's function.

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