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This is a copy of Math StackExchange question #4395977, which I felt was more appropriate for MathOverflow. Note on terminology: "admissible", "$(^+)$-stable", and "$\Pi^1_1$-...

Reading Chapter V, pages (73-97) in Proof Theory (Springer, 1977), by Kurt Schütte, I have encountered a peculiar problem which puzzles me. On page 96, a map $\rm{Nr}:\overline{\rm{OT}}\rightarrow \...

I am looking for a characterization of the $Π_2$ statements provable in KP. Here, KP (often denoted KPω) is the Kripke-Platek set theory, including infinity and full induction on ordinals. Here is ...

Given a theory $T$, for arbitrary formulas $φ$ and $ψ$ that provably in $T$ denote an ordinal, set $[φ]_T < [ψ]_T$ iff provably in $T$, the ordinal denoted by $φ$ is less than the ordinal denoted ...

Ordinal analysis is typically described as characterizing recursive ordinals in a theory $T$, but there is a sense in which it can characterize all $T$-ordinals, even those that are nonrecursive. ...

If we work in this notation: $$C_0 (\alpha, \beta) = \beta \cup \lbrace 0 \rbrace$$ $$C_{n+1} (\alpha, \beta) = \lbrace \gamma + \delta, \omega^\gamma, \Omega_{\gamma}, I_{\gamma}, \psi_\pi(\eta) | \...