| On a Boolean-valued Model of the Strict Implication System(Continuous) |
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| 引用本文： | LI Na,LIU Hua-ke(1.Department of Philosophy,Nankai University,Tianjin 300071,China, 2. College of Mathematics and Information Science,Henan University,Kaifeng 475001,China). On a Boolean-valued Model of the Strict Implication System(Continuous)[J]. 数学季刊, 2004, 19(4) |
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| 作者姓名： | LI Na LIU Hua-ke(1.Department of Philosophy Nankai University Tianjin 300071 China 2. College of Mathematics and Information Science Henan University Kaifeng 475001 China) |
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| 作者单位： | 1.Department of Philosophy，Nankai University，Tianjin 300071，China; 2. College of Mathematics and Information Science，Henan University，Kaifeng 475001，China |
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| 基金项目： | SupportedbytheNationSocialScienceFoundationofChina(04BZX047)SupportedbyTianjinCitySocialScienceFoundationofChina(TJ03-ZX009) |
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| 摘 要： | The reference [4] proved the consistency of S1 and S2 among Lewis' five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S3, S4 and S5 in Lewis' five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S3 and P3, S4 and P4; (2) the modal systems P3 and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in VB. Hence, the paper proves: (a) ‖As31‖ = 1; (b) ‖AS41‖ = 1; (c) ‖AS5l‖ = 1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model VB of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis' the strict implication system S3, S4 and S5.
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On a Boolean-valued Model of the Strict Implication System(Continuous) |
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| LI Na,LIU Hua-ke. On a Boolean-valued Model of the Strict Implication System(Continuous)[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4) |
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| Authors: | LI Na LIU Hua-ke |
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| Abstract: | |
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| Keywords: | the strict implication system Boolean-valued model Boolean value |
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