徐利治,朱梧槚,袁相碗,郑毓信.论G?del不完备性定理[J].数学研究及应用,1981,1(1):151~162
论G?del不完备性定理
On G?del' s Imcompleteness Theorem
投稿时间:1980-11-27  
DOI:10.3770/j.issn:1000-341X.1981.01.019
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作者单位
徐利治 吉林大学 
朱梧槚 吉林大学 
袁相碗 南京大学 
郑毓信 南京大学 
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中文摘要:
      
英文摘要:
      The object of this expository paper is to disclose the real essential idea involved in G?del's imcompleteness theorem through a detailed analysis of the proof presented in Arbib's booklet. In §1 very extensive definitions have been given of the potential infinite and the real infinite, respectively. In §2 the general concept concerning types of infinite extension processes as well as the principle of relatively complete exhaustion have been expounded. In§3 a deeper analysis has been made of the well-known proof of G?del's imcompleteness theorem, thus leading to the conclusion that G?del's theorem is actually implied by the most general principle that any infinite process of lower type cannot exhaust and exhibit the whole content of the corresponding process with relatively higher type, where the words "exhaust" and "exhibit" may be given precise meanings in certain special cases including the case for G?del's arithmetic logic.
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