Acho que isso tem interesse aqui. Pelo visto, incompletude é mesmo o caso típico.
-------------------------------------------------------- Anyway I can share this with you. Consider the framework of ZFC and axiomatize game theory within it (we have done that in one of the Tsuji papers). We can write down a set - it's a set, yes - of expressions so that, if ZFC has a model with standard arithmetic: - All expressions in that set are interpreted as equilibria of a previously specified game in that model. - But for the r = 0 case, all remaining expressions are undecidable in the theory. This is in fact a ``counting'' theorem that gives a more precise assessment of the oft quoted slogan, ``almost everything turns out to be undecidable.'' This set can be made to have all sorts of nasty properties within and outside the arithmetical hierarchy (outside we'll need some extra stuff). Also, it sort of mirrors a result of Cris Calude's on the scarcity of theorems in (reasonable) enumerations of formulae in a formal theory with enough arithmetic, based on classical predicate calculus & a few more technical conditions.
_______________________________________________ Logica-l mailing list Logica-l@dimap.ufrn.br http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
