Second order theories with ordinals and elementary comprehension

@article{Jger1995SecondOT,
  title={Second order theories with ordinals and elementary comprehension},
  author={Gerhard J{\"a}ger and Thomas Strahm},
  journal={Arch. Math. Log.},
  year={1995},
  volume={34},
  pages={345-375}
}
We study elementary second order extensions of the theory ID1 of noniterated inductive definitions and the theory PAs? of Peano arithmetic with ordinals. We determine the exact proof-theoretic strength of those extensions and their natural subsystems, and we relate them to subsystems of analysis with arithmetic comprehension plus H~ comprehension and bar induction without set parameters. 

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References

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Showing 1-10 of 12 references

About the prooftheoretic ordinals of weak xed pointtheories

  • W. Pohlers
  • Journal of Symbolic Logic
  • 1992

Iterated inductive fixed-point theories: applications to Hancock's conjecture

  • S. Feferrnan
  • The Patras Symposium,
  • 1982

Iterated inductive xedpoint theories : applications to Hancock ' sconjecture

  • G. Metakides
  • 1982

Beweistheorie von KPN

  • G. Jiger
  • Arch. Math. Logik Grundlagenforsch
  • 1980

Formal theories for transfinite iterations of generalized inductive definitions and some subsystems of analysis

  • S. Feferman
  • Intuitionism and Proof Theory. Proceedings of the…
  • 1968

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