| 命题逻辑中极大和谐理论之集上的拓扑与Cantor三分集 |
| |
| 引用本文： | 王国俊,王伟,宋建社.命题逻辑中极大和谐理论之集上的拓扑与Cantor三分集[J].陕西师范大学学报,2007,35(2):1-5. |
| |
| 作者姓名： | 王国俊 王伟 宋建社 |
| |
| 作者单位： | 陕西师范大学数学与信息科学学院 陕西西安710062(王国俊)，西安财经学院信息与教育技术中心 陕西西安710062(王伟)，西安高技术研究所 陕西西安710025(宋建社) |
| |
| 摘 要： | 从结构上清楚地描述了极大和谐理论的构造,证明了一个理论是极大和谐的当且仅当它是文字序列的逻辑闭包;在全体极大和谐理论之集上通过自然的方式引入了一种紧Hausdorff拓扑,证明了所得拓扑空间与Cantor三分集同胚.作为应用,给出了命题逻辑系统完备性的一个简单证明.
|
| 关 键 词： | 数理逻辑 极大和谐理论 紧Hausdorff标准拓扑 Cantor三分集 完备性 |
| 文章编号： | 1672-4291（2007）02-0001-05 |
| 修稿时间： | 2007-04-09 |
Topology on the set of maximal consistent propositional theories and the Cantor ternary set |
| |
| WANG Guo-jun,WANG Wei,SONG Jian-she.Topology on the set of maximal consistent propositional theories and the Cantor ternary set[J].Journal of Shaanxi Normal University: Nat Sci Ed,2007,35(2):1-5. |
| |
| Authors: | WANG Guo-jun WANG Wei SONG Jian-she |
| |
| Abstract: | Clearly described the structure of the set consisting of all maximal consistent propositional theories,and it is proved that a logic theory is maximal consistent if and only if it is a closure of a sequence of literals.In a natural way,a compact Hausdorff topology is introduced,and it is proved that the obtained topological space is homeomorphic to the Cantor ternary set.As an application,a simple proof of a complete theorem is proposed. |
| |
| Keywords: | mathematical logic maximal consistent theory compact Hausdorff standard topology Cantor ternary set completeness |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
