what is the proof-theoretic ordinal for $PA+TI(\epsilon_0)$, where $PA+TI(\epsilon_0)$ is Peano arithmetic where transfinite induction up to $\epsilon_0$ was added? Is it known?
Thank you
2026-03-29 23:26:58.1774826818
What is the proof-theoretic ordinal of $PA+TI(\epsilon_0)$?
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Based on the article "Beweistheoretische Erfassung der unendlichen Induktion in der Zahlentheorie" von Kurt Schütte (Mathematische Annalen 122, 1951, pp. 369-389), the proof-theoretic ordinal for PA+TI($\epsilon_0$) should be $\epsilon_1$.