| Popis: |
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. |
