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Notes
- 1.
\({\mathscr {T}}\) is \(\varDelta ^{0}_{2}\) and the left-most path \({\mathscr {P}}\) is \(\varDelta ^{0}_{2}\) in \({\mathscr {T}}\). Hence \({\mathscr {P}}\) is \(\varDelta ^{0}_{3}\).
- 2.
We can restrict C to \(\varPi ^{0}_{2}\)-formulas.
Reference
Hájek, P., Pudlák, P.: Metamathematics of first-order arithmetic. Perspectives in Mathematical Logic. Springer, Berlin (1993)
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Arai, T. (2020). Answers to Exercises. In: Ordinal Analysis with an Introduction to Proof Theory. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-6459-8_7
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