摘要
拓扑系统是Steven Vikers将拓扑的方法与数理逻辑理论的结果相结合于专著"Topology via Logic"中建立的一种新型的格论研究对象,并将这一理论应用于计算机理论的研究.本文借助于拓扑系统的思想和方法,以及Frame结构和Heyting代数的共有性质,以Heyting代数为主体建立了一种新型的逻辑代数系统-Heyting系统,并建立了Heyting系统之间的H-连续映射,给出了Heyting系统的H-locale化形式,并讨论了相关性质.
Topological system has been proposed by Steven Vikers in his work ＂Topology via Logic＂ through synthesizing the methods of topology and the theory of logics,which also is applied to study of computers theory.In the present paper,the new algebras system-Heyting system is put forward with the help of the idea of topological system and the properties enjoyed by Frame structure and Heyting algebras, which takes the Heyting algebras as its principal body;the H-continuous mapping connecting Heyting systems is established;the H-Localification of Heyting system is given,and the related properties are investigated.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2012年第6期1119-1130,共12页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(11171196)
