| On a Boolean-valued Model of the Strict Implication System(Continuous) |
| |
| 作者姓名： | LI Na LIU Hua-ke |
| |
| 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 |
| |
| 基金项目： | SupportedbytheNationSocialScienceFoundationofChina(04BZX047)
SupportedbyTianjinCitySocialScienceFoundationofChina(TJ03-ZX009) |
| |
| 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.
|
On a Boolean-valued Model of the Strict Implication System(Continuous) |
| |
| 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). |
| |
| Authors: | LI Na LIU Hua-ke |
| |
| Abstract: | |
| |
| Keywords: | the strict implication system Boolean-valued model Boolean value |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
