By restricting the common replacement axiom schema of ZF to ∑~M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called them ZF^M.Zhao Xi shun show that the c...By restricting the common replacement axiom schema of ZF to ∑~M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called them ZF^M.Zhao Xi shun show that the consistency of ZF^M can be deducted from ZF.Professor Zhang Jinwen raised the question whether the consistency of ZF^M can be deducted from ZF^(M+m(M)) for some m(n)≥1.In this paper,we get a positive solution to Professor Zhang's problem.Moreover,we show that the consistency of ZF^M can be deducted from ZF^(M+3).展开更多
文摘By restricting the common replacement axiom schema of ZF to ∑~M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called them ZF^M.Zhao Xi shun show that the consistency of ZF^M can be deducted from ZF.Professor Zhang Jinwen raised the question whether the consistency of ZF^M can be deducted from ZF^(M+m(M)) for some m(n)≥1.In this paper,we get a positive solution to Professor Zhang's problem.Moreover,we show that the consistency of ZF^M can be deducted from ZF^(M+3).
