A note on iterated consistency and infinite proofs View Full Text


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Article Info

DATE

2019-05

AUTHORS

Anton Freund

ABSTRACT

Schmerl and Beklemishev’s work on iterated reflection achieves two aims: it introduces the important notion of Π10-ordinal, characterizing the Π10-theorems of a theory in terms of transfinite iterations of consistency; and it provides an innovative calculus to compute the Π10-ordinals for a range of theories. The present note demonstrates that these achievements are independent: we read off Π10-ordinals from a Schütte-style ordinal analysis via infinite proofs, in a direct and transparent way. More... »

PAGES

339-346

References to SciGraph publications

  • 1991-09. Notation systems for infinitary derivations in ARCHIVE FOR MATHEMATICAL LOGIC
  • 2003-08. Proof-theoretic analysis by iterated reflection in ARCHIVE FOR MATHEMATICAL LOGIC
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00153-018-0639-y

    DOI

    http://dx.doi.org/10.1007/s00153-018-0639-y

    DIMENSIONS

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