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PROOF-THEORETIC STRENGTHS OF WEAK THEORIES FOR POSITIVE INDUCTIVE DEFINITIONS

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Publication:4692081
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DOI10.1017/jsl.2018.36zbMath1502.03021arXiv1603.01342OpenAlexW2963005337MaRDI QIDQ4692081

Toshiyasu Arai

Publication date: 26 October 2018

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01342

zbMATH Keywords

predicativityproof-theoretic ordinals


Mathematics Subject Classification ID

Second- and higher-order arithmetic and fragments (03F35) Recursive ordinals and ordinal notations (03F15)




Cites Work

  • Unnamed Item
  • An order-theoretic characterization of the Howard-Bachmann-hierarchy
  • A new system of proof-theoretic ordinal functions
  • Proof-theoretic investigations on Kruskal's theorem
  • Bar induction and \(\omega\) model reflection
  • A note on the theory of positive induction, \({{\text{ID}}^*_1}\)
  • The proof-theoretic analysis of transfinitely iterated quasi least fixed points
  • Some theories with positive induction of ordinal strength φω0
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