A note on iterated consistency and infinite proofs

Archive for Mathematical Logic 58 (3-4):339-346 (2019)
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Abstract

Schmerl and Beklemishev’s work on iterated reflection achieves two aims: it introduces the important notion of \-ordinal, characterizing the \-theorems of a theory in terms of transfinite iterations of consistency; and it provides an innovative calculus to compute the \-ordinals for a range of theories. The present note demonstrates that these achievements are independent: we read off \-ordinals from a Schütte-style ordinal analysis via infinite proofs, in a direct and transparent way.

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10.1007/s00153-018-0639-y

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References found in this work

Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.Georg Kreisel & Azriel Lévy - 1968 - Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
Proof-theoretic analysis by iterated reflection.Lev D. Beklemishev - 2003 - Archive for Mathematical Logic 42 (6):515-552.
Notation systems for infinitary derivations.Wilfried Buchholz - 1991 - Archive for Mathematical Logic 30 (5-6):277-296.
Iterated reflection principles and the ω-rule.Ulf R. Schmerl - 1982 - Journal of Symbolic Logic 47 (4):721-733.

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