IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-49424-7_3.html
   My bibliography  Save this book chapter

… and so on: Schütte on Naming Ordinals

In: The Legacy of Kurt Schütte

Author

Listed:
  • John N. Crossley

    (Monash University, Faculty of Information Technology)

Abstract

Kurt Schutte 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 Schutte’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 Schutte 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 ‘natural’ but the quest to characterise ‘natural wellorderings’ (or even their extent) seems illusory, but Schutte only needed a limited range of ordinals, which he treated elegantly.

Suggested Citation

  • John N. Crossley, 2020. "… and so on: Schütte on Naming Ordinals," Springer Books, in: Reinhard Kahle & Michael Rathjen (ed.), The Legacy of Kurt Schütte, chapter 0, pages 37-46, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-49424-7_3
    DOI: 10.1007/978-3-030-49424-7_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-030-49424-7_3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.