On a proof-theoretical analysis of Σ11-AC, Σ11-DC and Δ11-CA

  • Sergei Tupailo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 822)


We present a simple method of embedding of δ 1 1 -CA, σ 1 1 -AC and σ 1 1 -DC into \(RA_{\varepsilon _0 } ,(RA + PAC)_{\varepsilon _0 }\), and \((RA + PDC)_{\varepsilon _0 }\) respectively, where PAC is Predicative Axiom of Choice and PDC is Predicative Axiom of Dependent Choice, These ramified systems are known to have proof-theoretic ordinals Φε00, which in the case of PAC and PDC can be proved by normalization of Ramified Analysis with Hilbert's epsilon-symbol. In all cases (particularly, of δ 1 1 -CA) our embedding is straightforward and avoids any intermediate steps (like σ 1 1 -Reflection), which was always the case before.


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    K. Schütte: Proof Theory. Springer, 1977Google Scholar
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    G. Jäger, K. Schütte: Eine syntaktische Abrenzung der (δ11-CA)-Analysis. In: Bayerische Akademie der Wissenschaften, Sitzungsberichte, Munich, J. 1979, 15–34.Google Scholar
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    S. Tupailo: Normalization for Ramified Analysis with Hilbert's Epsilon-Symbol, to be published.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Sergei Tupailo
    • 1
  1. 1.Department of MathematicsStanford UniversityStanford

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