摘要
在前期一系列论文及著作中([2][4][5])对实数集(连续统)的可数性、康托对角线法等问题充分讨论的基础上,对序数的可数性问题进行分析,并由此引出对ZFC公理系统中的正则公理(基础公理,限制公理)的讨论。对与斯梅尔第18问题密切相关的哥德尔定理进行了分析,得到全新结论。提出实数的一进制表示法并在此基础上讨论康托对角线法的局限性问题。
On the basis of the previous discussions about the countability of continuum,Cantor diagonal method,etc.in a series of papers and books,the article analyzes the countability of ordinal number and axiom of regularity in ZFC axiomatic system.It also discusses Gdel's incompleteness theorem which is closely related to Smale's 18th question and reaches a brand-new conclusion.
出处
《天津职业院校联合学报》
2011年第5期51-62,共12页
Journal of Tianjin Vocational Institutes
关键词
序数
康托对角线法
连续统
可数
正则公理
哥德尔定理
一进制实数
直觉主义悖论
丘奇悖论
ordinal number
Cantor diagonal method
continuum
countable
axiom of regularity
Gdel's incompleteness theorem
real number of the unitary system
paradox of intuitionalism
paradox of Church