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 language | English |
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Title of host publication | The Legacy of Kurt Schütte |
Editors | Reinhard Kahle, Michael Rathjen |
Place of Publication | Cham Switzerland |
Publisher | Springer |
Chapter | 3 |
Pages | 37-46 |
Number of pages | 10 |
Edition | 1st |
ISBN (Electronic) | 9783030494247 |
ISBN (Print) | 9783030494230 |
DOIs | |
Publication status | Published - 2020 |