| 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 |
| 中文关键词: |
| 英文关键词: |
| 基金项目: |
|
| 摘要点击次数: 2343 |
| 全文下载次数: 2043 |
| 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. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|
