… and so on: Schütte on Naming Ordinals

John N. Crossley ()
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John N. Crossley: Monash University, Faculty of Information Technology

Chapter Chapter 3 in The Legacy of Kurt Schütte, 2020, pp 37-46 from Springer

Abstract: 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-49424-7_3

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DOI: 10.1007/978-3-030-49424-7_3

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