Proof-theoretic analysis of KPM

@article{Rathjen1991ProoftheoreticAO,
  title={Proof-theoretic analysis of KPM},
  author={M. Rathjen},
  journal={Archive for Mathematical Logic},
  year={1991},
  volume={30},
  pages={377-403}
}
  • M. Rathjen
  • Published 1991
  • Mathematics, Computer Science
  • Archive for Mathematical Logic
  • AbstractKPM is a subsystem of set theory designed to formalize a recursively Mahlo universe of sets. In this paper we show that a certain ordinal notation system is sufficient to measure the proof-theoretic strength ofKPM. This involves a detour through an infinitary calculus RS(M), for which we prove several cutelimination theorems. Full cut-elimination is available for derivations of $$\Sigma (L_{\omega _1^c } )$$ sentences, whereω1c denotes the least nonrecursive ordinal. This paper is self… CONTINUE READING
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    References

    SHOWING 1-10 OF 17 REFERENCES
    Ordinal notations based on a hierarchy of inaccessible cardinals
    • W. Pohlers
    • Mathematics, Computer Science
    • Ann. Pure Appl. Log.
    • 1987
    • 8
    Proof Theory: An Introduction
    • 130
    ϱ-inaccessible ordinals, collapsing functions and a recursive notation system
    • G. Jäger
    • Mathematics, Computer Science
    • Arch. Math. Log.
    • 1984
    • 19
    A new system of proof-theoretic ordinal functions
    • W. Buchholz
    • Mathematics, Computer Science
    • Ann. Pure Appl. Log.
    • 1986
    • 70
    • PDF
    The Incompleteness Theorems
    • 279
    Proof theory and ordinal analysis
    • W. Pohlers
    • Mathematics, Computer Science
    • Arch. Math. Log.
    • 1991
    • 35
    Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Bäume
    • S. Simpson
    • Mathematics, Computer Science
    • Arch. Math. Log.
    • 1985
    • 34
    • PDF
    Ein Mengensystem ohne Kollabierungsfunktionen. Oberseminarvortrag
    • Miinchen
    • 1984