文章摘要
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
  
DOI:
中文关键词: 正则互摸拟  非良基公理  非良基集合
英文关键词: regular bisimulation  non-well-founded axioms  non-well-founded sets
基金项目::国家社科基金项目(12BZX060)
作者单位
姚从军1,2 1.湖南科技学院 思政部湖南 永州 4251992.中国社会科学院 哲学所北京 100732 
杨红梅1,2,马跃如1 1.中南大学 商学院湖南 长沙 4111012.湘潭大学 研究生院湖南 湘潭 411105 
杨俊明 湖南师范大学 历史文化学院湖南 长沙 410081 
唐松林,刘静 湖南大学 教育科学研究院湖南 长沙 410082 
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中文摘要:
      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。
英文摘要:
      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≌t and 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.
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