数学季刊 ›› 1993, Vol. 8 ›› Issue (3): 7-12.

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On the Consistency of ZFn in ZFn+3

  

  1. Inst. of software Academia Sinica,,Beijing 100080

  • 收稿日期:1990-04-25 出版日期:1993-09-30 发布日期:2025-05-27

On the Consistency of ZFn in ZFn+3

  1. Inst. of software Academia Sinica,,Beijing 100080
  • Received:1990-04-25 Online:1993-09-30 Published:2025-05-27

摘要: 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 themZFM. Zhao Xi shun show that the consistency of ZFM can be deducted from ZF. Professor ZhangJinwen raised the question whether the consistency of ZFM can be deducted from ZFM+m(M) for somem(n)≥1. In this paper,we get a positive solution to Professor Zhang's problem.Moreover,weshow that the consistency of ZFM can be deducted from ZFM+3

关键词: set theory, consistency, reflection, truth defintion

Abstract: 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 themZFM. Zhao Xi shun show that the consistency of ZFM can be deducted from ZF. Professor ZhangJinwen raised the question whether the consistency of ZFM can be deducted from ZFM+m(M) for somem(n)≥1. In this paper,we get a positive solution to Professor Zhang's problem.Moreover,weshow that the consistency of ZFM can be deducted from ZFM+3

Key words: set theory, consistency, reflection, truth defintion