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Zur Beweistheorie von KP+ $$ \varPi_{3} $$ -Ref

In: The Legacy of Kurt Schütte

Author

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  • Kurt Schütte

    (Mathematisches Institut, LMU)

Abstract

This article together with the foregoing on KPM belongs to the last two papers Schütte wrote on ordinal analysis. It is from 1992 and deals with the strongest system for which an ordinal analysis was available at the time: Kripke-Platek set theory with $$ \varPi_{3} $$ -reflection. A crucial tool is the stationary collapsing technique. Schütte sketches a modified treatment of the analysis given in Rathjen’s Habilitationschrift [1], later published as [2]. Schütte furnishes a very elegant treatment in his calculus of positive and negative forms, making direct use of structural inferences that are harder to engineer in a sequent calculus. Moreover, he achieves the operator control on derivations in a very economical way. Skizzierung einer modifizierten Fassung der beweistheoretischen Analyse von KP+ $$ \varPi_{3} $$ -Ref nach M. Rathjen. Die Beweise der hier zusammengestellten Lemmata sind, soweit sie nicht ausgeführt sind, entweder wohlbekannt oder der Habilitationsschrift [1] von M. Rathjen zu entnehmen.

Suggested Citation

  • Kurt Schütte, 2020. "Zur Beweistheorie von KP+ $$ \varPi_{3} $$ -Ref," Springer Books, in: Reinhard Kahle & Michael Rathjen (ed.), The Legacy of Kurt Schütte, chapter 0, pages 485-502, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-49424-7_25
    DOI: 10.1007/978-3-030-49424-7_25
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