无限格与其非标准扩张  

Infinite Lattice and Its Nonstandard Extension

作　　者：马春晖[1,2] 史艳维[3] 李生刚[2] 李体政[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]陕西师范大学数学与信息科学学院,陕西西安710062 [3]西安培华学院基础部,陕西西安710125

出　　处：《模糊系统与数学》2012年第6期92-97,共6页Fuzzy Systems and Mathematics

基　　金：陕西省自然科学基金资助项目(2007A12);陕西省教育厅专项科研项目(11JK0495;11JK0507)

摘　　要：在非标准κ-饱和模型下,研究了无限格L的非标准扩张*L的性质及其在L-集滤子理论中的应用。首先,定义了κ-完备格的概念,讨论了完备格与κ-完备格之间的关系,证明了无限格L的非标准扩张*L是κ-完备格。其次,定义了L-集滤子的单子,利用κ-完备格证明了此定义是合理的。最后,利用L-集滤子的单子给出了L-集滤子族上确界存在的充分且必要条件。The main purpose of this paper is to research the properties of ＊L, which is the nonstandard extension of infinite lattice L, and its applications to L--sets filter in nonstandard κ-saturated model, Firstly, the notion of κ-complete lattice is proposed and the differences with complete lattice are shown, and it is obtained that L is a κ-complete lattice. Then the monad of L--sets filter is well-defined by κ-complete lattice. Finally, the necessary and sufficient condition of existence of the supremum of a family of L--sets filters is proved by their monads.

关 键 词：非标准κ-饱和模型 κ-完备格 单子 上确界 

分 类 号：O141[理学—数学]