摘要
本组系列论文 ( )～ ( )从数学和认识论的角度系统地研究了无穷观问题的历史发展和现状 ,确立了无穷观背景世界的三分法原则 ,指出了两种无穷观相互排斥的局限性 ,形成了统一两种无穷于同一框架中的基本观点 ,并建立了一个统一实无限与潜无限于同一框架中的公理集合论系统 APAS。
In a view of mathematics and epistemology, in the series of papers from (Ⅰ) to (Ⅴ), the historical background and current situation of the problem of the infinity are reviewed, the restriction of the repellency of two existing views on the infinity is pointed out, an outlook on the infinity to unify the actual infinity and the potential infinity into one framework is presented, and an axiomatic system of the sets is established based on such a framework.
出处
《南京航空航天大学学报》
EI
CAS
CSCD
北大核心
2002年第4期312-317,共6页
Journal of Nanjing University of Aeronautics & Astronautics
关键词
无穷观
实无限
潜无限
公理集合论系统
APAS
potential infinity
actual infinity
axiomatic set theory
natural number system
diagonal method
intuitionism
