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A note on iterated consistency and infinite proofs

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Abstract

Schmerl and Beklemishev’s work on iterated reflection achieves two aims: it introduces the important notion of \(\varPi ^0_1\)-ordinal, characterizing the \(\varPi ^0_1\)-theorems of a theory in terms of transfinite iterations of consistency; and it provides an innovative calculus to compute the \(\varPi ^0_1\)-ordinals for a range of theories. The present note demonstrates that these achievements are independent: we read off \(\varPi ^0_1\)-ordinals from a Schütte-style ordinal analysis via infinite proofs, in a direct and transparent way.

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  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289, Darmstadt, Germany

    Anton Freund

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  1. Anton Freund
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Correspondence to Anton Freund.

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Freund, A. A note on iterated consistency and infinite proofs. Arch. Math. Logic 58, 339–346 (2019). https://doi.org/10.1007/s00153-018-0639-y

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  • DOI: https://doi.org/10.1007/s00153-018-0639-y

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