非良基公理和非良基集合论的域  

The Non-Well-Founded Axioms and the Ranges of Non-Well-Founded Sets

作　　者：姚从军[1,2] 

机构地区：[1]湖南科技学院思政部,湖南永州425199 [2]中国社会科学院哲学所,北京100732

出　　处：《湖南科技大学学报（社会科学版）》2014年第1期33-40,共8页Journal of Hunan University of Science and Technology(Social Science Edition)

基　　金：国家社科基金项目(12BZX060)

摘　　要：正则互模拟是非良基公理和非良基集合论形成的基础,基于正则互模拟形成了一簇非良基公理。定义了三种正则互模拟≌*、≌t和≡V0,由它们生成的非良基公理AFA≌*、AFA≌t和AFA≡V0与经典的非良基公理FAFA、SAFA和AFA分别等价;非良基公理FAFA和AFA位于非良基公理簇的两端,SAFA处于FAFA和AFA之间;非良基公理FAFA、SAFA和AFA两两不相容;与非良基公理FAFA、SAFA、AFA相对应的外延力依次增强,而相对应的非良基集合论的域依次缩小。Regular bisimulation is the foundation of the non- well- founded axioms and the non- well-founded set theories,and a family of non- well- founded axioms are based on it. This paper defines the regular bisimulations≌*,≌t and ≡ V0,shows the non- well- founded axioms AFA≌*,AFA≌tand AFA≡V0crrosponding to them are respectively equal to the non- well- founded axioms FAFA,SAFA and AFA; FAFA and AFA are at both ends of the family of non- well- founded,SAFA between them,and FAFA,SAFA and AFA are pairwise incompatible; The extensionalities of FAFA,SAFA and AFA increase incrementally,and their ranges decrease successively.

关 键 词：正则互摸拟 非良基公理 非良基集合 

分 类 号：B81[哲学宗教—逻辑学]