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- W56358913 abstract "Through his own contributions (individual and collaborative) and his extraordinary personal influence, Georg Kreisel did perhaps more than anyone else to promote the development of proof theory and the metamathematics of constructivity in the last forty-odd years. My purpose here is to give some idea of just one aspect of Kreisel’s contributions to these areas, namely that devoted to “unwinding” the constructive content of prima-facie nonconstructive mathematical proofs. This program was the subject of his first remarkable papers in the 1950’s, and it has drawn his repeated attention ever since. Anyone who is familiar with even a small part of Kreisel’s writings knows that he inverts the usual ratio of technical work to discussion. He takes much greater pains to explain, at length, the significance of the work than to set it out in an organized step-by-step fashion. His attitude seems to be that if one has the right ideas, the details will look after themselves. And they did amazingly often (or, he could rely on more disciplined collaborators to look after them). However, in the specific area dealt with here, there are several important cases where the expected details are either problematic or simply missing. This can’t help but affect my main aim here, which is to assess whether the work on Kreisel’s unwinding program, both his own and that of others, lives up to its claims. My overall conclusion is that while the general theory of unwinding launched by Kreisel is eminently successful, the supposed applications to date are few and far between; moreover, in some prominent cases, their status even as applications has to be put in question." @default.
- W56358913 created "2016-06-24" @default.
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- W56358913 date "2002-01-01" @default.
- W56358913 modified "2023-09-27" @default.
- W56358913 title "Kreisel’s “unwinding” program" @default.
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