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Ein Wohlordnungsbeweis für das OrdinalzahlensystemT(J)

A proof of the wellordering of the ordinal number systemT(J)

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Summary

A recursive notation system of a strong segment of ordinals was developped by Jäger [3]. An unessential modified versionT(J) of this notation system was described in [4]. In the following, the well-ordering ofT(J) is proved in a formal system of second order arithmetic with the axiom schema ofΠ 12 -comprehension. It follows, that the proof theoretical ordinal ofΠ 12 -analysis is greater than the order type ofT(J).

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Literatur

  1. Buchholz, W.: Normalfunktionen und konstruktive Systeme von Ordinalzahlen. Proof Theory Symposion Kiel 1974. Lect. Notes Math.500, 4–25 (1975)

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  2. Buchholz, W.: Wohlordnungsbeweise mittels Hauptfolgen. Oberseminarvortrag München 1986

  3. Jäger, G.:ϱ-Inaccessible ordinals, collapsing functions and a recursive notation system. Arch. Math. Logik Grundlagenforsch.24, 49–62 (1984)

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  4. Schütte, K.: Majorisierungsrelationen und Fundamentalfolgen eines Ordinalzahlensystems von G. Jäger. Arch. Math. Logik Grundlagenforsch.26, 29–55 (1986/87)

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Authors and Affiliations

  1. Mathematisches Institut, Universität München, Theresienstraße 39, D-8000, München, Bundesrepublik Deutschland

    K. Schütte

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  1. K. Schütte
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Schütte, K. Ein Wohlordnungsbeweis für das OrdinalzahlensystemT(J) . Arch Math Logic 27, 5–20 (1988). https://doi.org/10.1007/BF01625829

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  • DOI: https://doi.org/10.1007/BF01625829

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