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Please see [[User:JRSpriggs/Ordinal notation]]. [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 18:41, 2 April 2022 (UTC)
== Possible error in example ψ?==
Before we introduce the simultaneous recursion, there is a circular reference via ψ<sub>1</sub>. We define ψ<sub>0</sub>(α) using a set C<sub>0</sub>(α), which includes the ordinal ψ<sub>0</sub>(α+2). However, ψ<sub>1</sub>(α+2) is defined using a set C<sub>1</sub>(α+2), which contains ψ<sub>0</sub>(α0+1), which means ψ is defined by a non-terminating inductive clause. So I think this version of ψ is not just hard to extend as mentioned in the article, but actually not a well-defined system of functions. I'm not sure how it should be fixed while keeping its current purpose, an intermediate strengthening of ψ which is meant to lead into the system with arbitrarily many ψ-functions. [[User:C7XWiki|C7XWiki]] ([[User talk:C7XWiki|talk]]) 22:13, 25 September 2022 (UTC)
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