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I asked this question on MSE some days ago but I have not received any answer so I have decided to post it here. I would like to consider a generalization of the notation $\Pi$ and $\Sigma$ used for ...

Question: What are some natural examples of recursive pseudowellorderings? By natural, I mean in the style of reasonable ordinal notation systems as opposed to dependent on a Gödel numbering or an ...

In a previous MO question, I was told by several commenters that (a) it's known that there exists a computable ordinal $\alpha_{ZF}$ that "encodes the strength of ZF set theory" (i.e., a least ...