摘要
首先给出了中介逻辑ＭＬ的二值子系统ＦＩ＊ＭＬ，说明了它与经典二值逻辑的子系统ＦＩ＊同构。其次，利用中介公理集合论ＭＳ的相关理论，构造了ＭＳ中的自然数系统，证明了Ｐｅａｎｏ５条公理为ＭＳ中的定理。最后指出以此五条性质为公理，并以ＦＩ＊ＭＬ为配套逻辑，在ＭＳ中可推出自然数的所有性质。这表明Ｐｅａｎｏ自然数系统能在ＭＳ中产生，为最终证明精确性经典数学能奠基于ＭＳ提供了理论基础。
Firstly, presents F I ML which is a two valued subsystem of medium logic, and shows that F I ML is isomorphic with F I which is a subsystem of classical two valued logic. Secondly, by using of the medium axiomatic set theory (MS), a natural number system in MS is constructed, and it is proved that five axioms of Peano′s natural number system are theorems is MS. Finally, it is pointed out that all properties of Peano′s natural number may be entailed in MS, when one relies on combining these five theorems with F I ML . All of these indicate that the system of Peano′s natural number can be generated in MS and a theoretical foundation provided to prove that MS is a foundation of classical mathematics.
出处
《南京航空航天大学学报》
EI
CAS
CSCD
北大核心
1997年第2期179-184,共6页
Journal of Nanjing University of Aeronautics & Astronautics
基金
国家攀登计划
国家高技术863计划资助
关键词
数理逻辑
自然数系统
公理集合论
中介逻辑
mathematical logic
mathematical theories
natural number system
axiomatic set theory
medium logic
axiomatic medium set theory
