… and so on: Schütte on Naming Ordinals

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    Abstract

    Kurt Schütte prized elegance in his work. Ever since the work of Gerhard Gentzen, ordinal numbers have been used as a measure in developing consistency proofs for ever more powerful theories. Here I discuss Schütte’s development of his elegant systems of recursive ordinal notations, whichwent through a small number of phases, but the central idea for his systems of ordinal notation originated from a 1908 paper of Oswald Veblen. However Schütte did not immediately reveal how he had arrived at his quite complicated notations; he simply presented his Klammersymbolen as a fait accompli. This chapter aims at clarifying the development. Further, when Veblen’s technique is viewed as a process, the systems can be extended much further. Successive processes seem ʼnatural’ but the quest to characterise ʼnatural wellorderings’ (or even their extent) seems illusory, but Schütte only needed a limited range of ordinals, which he treated elegantly.

    Original languageEnglish
    Title of host publicationThe Legacy of Kurt Schütte
    EditorsReinhard Kahle, Michael Rathjen
    Place of PublicationCham Switzerland
    PublisherSpringer
    Chapter3
    Pages37-46
    Number of pages10
    Edition1st
    ISBN (Electronic)9783030494247
    ISBN (Print)9783030494230
    DOIs
    Publication statusPublished - 2020

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