| [ KAIST ] in KIDS 글 쓴 이(By): seik (daria) 날 짜 (Date): 2003년 3월 15일 토요일 오전 09시 41분 32초 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. --- axiom system이 뭘 말하는것인가요? axiom of choice를 뺀 axiom set을 말하는것입니까? transfinite induction과 axiom of choice는 equivalent하지 않나요? 아직도 axiom of choice에 대한 dissent가 수학계에 남아있습니까? 궁금하군요. 전 뭘 증명할때 이때것(학부/대학원 초기시절 숙제할때 빼고는) axiom of choice를 쓴적이 없어서, 이놈의 필수 불가결성을 뼈저리게 모릅니다. @Hey MTV guys, make Daria Morgendorffer DVD series! |