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$\omega^{CK}_1$ is the supremum of all the recursive ordinals, where an ordinal $\alpha$ is recursive if there is a computable ordering of a subset of the naturals with order type $\alpha$. For a ...

$\DeclareMathOperator{\address}{address}$ As in my other question, it is assumed that the (total) function describing a given notation is denoted as $\address:p \rightarrow \Bbb{N}$ and assumed to be ...

Sometime around 1975, Leo Harrington wrote a set of notes, apparently 13 pages long, entitled Kolmogorov's $R$-operator and the first nonprojectible ordinal. I do not know how widely they were ...