User blog comment:Ubersketch/A proposal for a standard/@comment-35470197-20190811012241/@comment-35470197-20190813002934

It might be just a kind of typo, but Ω_a = ψ_a(0) (not ψ_{a+1}(0)). For example, we have Ω_1 = ψ_1(0) like usual Buchholz's OCF.

So the inequality should be corrected to be a <= b. It is true that the equality holds only when c = 0. You are able to prove this from the definition, but I think that the majority here are not.

I know that they can understand the criterion, if they hear it. It does not mean that they can completely write down the algorithm to determine the <-relation for a general pair of expressions of ordinals. That is why it can be a problem. If we do not explicitly write down the whole algorithm, people will unintensionally fill the brank with their intuision. For example, they would compute like "ψ_0(ψ_1(ψ_2(ψ_3(0)))) = ψ_0(Ω_3)", if we do not show an explicit algorithm to compute standard forms or to compute orders or equalities.