| [ KAIST ] in KIDS 글 쓴 이(By): guest (guest) <218.236.132.103> 날 짜 (Date): 2003년 3월 14일 금요일 오후 10시 49분 21초 제 목(Title): Re: 일더하기 일은 이의 증명 Yes, arguably most mathematical theories can be expressed in set theory. But the problem is that in this case we are not talking about set theory, but a formal system for arithmetic. There _are_ pure number theoretic statements that can be proved using transfinite induction but cannot be proved without it. (To be precise: it is proved that they cannot be proved without transfinite induction.) And of course in the given system there's no transfinite induction in the language. What I'm saying is that the system discussed here might not be powerful enough to cover all normal activities of number theoriests. |