Ordinal analyses for monotone and cofinal transfinite inductions

Archive for Mathematical Logic:1-15 (forthcoming)

We consider two variants of transfinite induction, one with monotonicity assumption on the predicate and one with the induction hypothesis only for cofinally many below. The latter can be seen as a transfinite analogue of the successor induction, while the usual transfinite induction is that of cumulative induction. We calculate the supremum of ordinals along which these schemata for \ formulae are provable in \. It is shown to be larger than the proof-theoretic ordinal \ by power of base 2. We also show a similar result for the structural transfinite induction, defined with fundamental sequences.
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DOI 10.1007/s00153-019-00688-5
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Proof-Theoretic Analysis by Iterated Reflection.Lev D. Beklemishev - 2003 - Archive for Mathematical Logic 42 (6):515-552.

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