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A note on iterated consistency and infinite proofs

  • Anton Freund
Article
  • 19 Downloads

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.

Keywords

Iterated consistency Ordinal analysis \(\varPi ^0_1\)-ordinal Infinite proofs \(\omega \)-rule Cut elimination 

Mathematics Subject Classification

03F05 03F25 03F15 03B30 03F30 

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References

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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