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arXiv · 1709.01540

A Note on Iterated Consistency and Infinite Proofs

Anton Freund
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Abstract

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

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Anton Freund. 2017-09-05. A Note on Iterated Consistency and Infinite Proofs. https://doi.org/10.1007/s00153-018-0639-y

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