Theories with Koenig ' S Lemma

نویسنده

  • Wilfried Sieg
چکیده

The problems I want to consider and the results I want to discuss are PRIMA FACI E of a very traditional proof theoretic sort: they concern the reduction of subsystems of second and higher order arithmetic to constructively unproblematic theories. The arguments for these results seem also to be of a traditional proof theoretic sort: they use formai and semiformal sequent calculi and exploit the fact thàt these calculi allow the elimination of cuts. There are, however, fascinating and significant twists ; namely, (i) the constructively unproblematic theories are ali fragments of elementary number theory, (ii) the subsystems are nevertheless sufficiently strong to serve as formai frames for large parts of mathematical analysis and algebra, and (iii) the arguments use systematically "derivations as computations" through a form of Herbrand's theorem. The latter slogan can be taken as the theme of the paper. [1]

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تاریخ انتشار 2008